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Theorem bnj1000 29289
 Description: Technical lemma for bnj852 29269. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1000.1
bnj1000.2
bnj1000.3
bnj1000.15
bnj1000.16
Assertion
Ref Expression
bnj1000
Distinct variable groups:   ,   ,   ,   ,   ,,   ,
Allowed substitution hints:   (,,,,)   (,,,)   (,,,,)   (,,,)   (,,,)   (,,,)   (,,,,)

Proof of Theorem bnj1000
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1000.2 . 2
2 df-ral 2561 . . . . 5
32bicomi 193 . . . 4
4 bnj1000.3 . . . 4
53, 4bnj524 29082 . . 3
6 nfv 1609 . . . . . . . 8
76sbc19.21g 3068 . . . . . . 7
84, 7ax-mp 8 . . . . . 6
9 nfv 1609 . . . . . . . . . 10
109sbc19.21g 3068 . . . . . . . . 9
114, 10ax-mp 8 . . . . . . . 8
12 fveq1 5540 . . . . . . . . . . 11
13 fveq1 5540 . . . . . . . . . . . 12
14 ax-17 1606 . . . . . . . . . . . . 13
15 bnj1000.16 . . . . . . . . . . . . . . . 16
16 nfcv 2432 . . . . . . . . . . . . . . . . 17
17 nfcv 2432 . . . . . . . . . . . . . . . . . . 19
18 bnj1000.15 . . . . . . . . . . . . . . . . . . . 20
19 nfiu1 3949 . . . . . . . . . . . . . . . . . . . 20
2018, 19nfcxfr 2429 . . . . . . . . . . . . . . . . . . 19
2117, 20nfop 3828 . . . . . . . . . . . . . . . . . 18
2221nfsn 3704 . . . . . . . . . . . . . . . . 17
2316, 22nfun 3344 . . . . . . . . . . . . . . . 16
2415, 23nfcxfr 2429 . . . . . . . . . . . . . . 15
25 nfcv 2432 . . . . . . . . . . . . . . 15
2624, 25nffv 5548 . . . . . . . . . . . . . 14
2726nfcrii 2425 . . . . . . . . . . . . 13
2814, 27bnj1316 29169 . . . . . . . . . . . 12
2913, 28syl 15 . . . . . . . . . . 11
3012, 29eqeq12d 2310 . . . . . . . . . 10
31 fveq1 5540 . . . . . . . . . . 11
32 fveq1 5540 . . . . . . . . . . . 12
33 ax-17 1606 . . . . . . . . . . . . 13
3433bnj956 29124 . . . . . . . . . . . 12
3532, 34syl 15 . . . . . . . . . . 11
3631, 35eqeq12d 2310 . . . . . . . . . 10
37 fveq1 5540 . . . . . . . . . . 11
38 fveq1 5540 . . . . . . . . . . . 12
39 ax-17 1606 . . . . . . . . . . . . 13
4039, 27bnj1316 29169 . . . . . . . . . . . 12
4138, 40syl 15 . . . . . . . . . . 11
4237, 41eqeq12d 2310 . . . . . . . . . 10
434, 30, 36, 42bnj610 29092 . . . . . . . . 9
4443imbi2i 303 . . . . . . . 8
4511, 44bitri 240 . . . . . . 7
4645imbi2i 303 . . . . . 6
478, 46bitri 240 . . . . 5
4847albii 1556 . . . 4
49 sbcalg 3052 . . . . 5
504, 49ax-mp 8 . . . 4
51 df-ral 2561 . . . 4
5248, 50, 513bitr4ri 269 . . 3
53 bnj1000.1 . . . 4
5453, 4bnj524 29082 . . 3
555, 52, 543bitr4ri 269 . 2
561, 55bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wceq 1632   wcel 1696  wral 2556  cvv 2801  wsbc 3004   cun 3163  csn 3653  cop 3656  ciun 3921   csuc 4410  com 4672  cfv 5271   c-bnj14 29029 This theorem is referenced by:  bnj965  29290 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-iun 3923  df-br 4040  df-iota 5235  df-fv 5279
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