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Theorem bnj1491 29428
 Description: Technical lemma for bnj60 29433. 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
bnj1491.1
bnj1491.2
bnj1491.3
bnj1491.4
bnj1491.5
bnj1491.6
bnj1491.7
bnj1491.8
bnj1491.9
bnj1491.10
bnj1491.11
bnj1491.12
bnj1491.13
Assertion
Ref Expression
bnj1491
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1491
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1491.13 . 2
2 bnj1491.1 . . . . 5
3 bnj1491.2 . . . . 5
4 bnj1491.3 . . . . 5
5 bnj1491.4 . . . . 5
6 bnj1491.5 . . . . 5
7 bnj1491.6 . . . . 5
8 bnj1491.7 . . . . 5
9 bnj1491.8 . . . . 5
10 bnj1491.9 . . . . 5
11 bnj1491.10 . . . . 5
12 bnj1491.11 . . . . 5
13 bnj1491.12 . . . . 5
142, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13bnj1466 29424 . . . 4
1514nfcii 2565 . . 3
164bnj1317 29195 . . . . . 6
1716nfcii 2565 . . . . 5
1815, 17nfel 2582 . . . 4
1915nfdm 5113 . . . . 5
2019nfeq1 2583 . . . 4
2118, 20nfan 1847 . . 3
22 eleq1 2498 . . . 4
23 dmeq 5072 . . . . 5
2423eqeq1d 2446 . . . 4
2522, 24anbi12d 693 . . 3
2615, 21, 25spcegf 3034 . 2
271, 26mpan9 457 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3a 937  wex 1551   wceq 1653   wcel 1726  cab 2424   wne 2601  wral 2707  wrex 2708  crab 2711  cvv 2958  wsbc 3163   cun 3320   wss 3322  c0 3630  csn 3816  cop 3819  cuni 4017   class class class wbr 4214   cdm 4880   cres 4882   wfn 5451  cfv 5456   c-bnj14 29054   w-bnj15 29058   c-bnj18 29060 This theorem is referenced by:  bnj1312  29429 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-xp 4886  df-dm 4890  df-res 4892  df-iota 5420  df-fv 5464
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