Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1491 Unicode version

Theorem bnj1491 29403
 Description: Technical lemma for bnj60 29408. 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 simpr 447 . 2
2 bnj1491.13 . . 3
32adantr 451 . 2
4 bnj1491.1 . . . . 5
5 bnj1491.2 . . . . 5
6 bnj1491.3 . . . . 5
7 bnj1491.4 . . . . 5
8 bnj1491.5 . . . . 5
9 bnj1491.6 . . . . 5
10 bnj1491.7 . . . . 5
11 bnj1491.8 . . . . 5
12 bnj1491.9 . . . . 5
13 bnj1491.10 . . . . 5
14 bnj1491.11 . . . . 5
15 bnj1491.12 . . . . 5
164, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15bnj1466 29399 . . . 4
1716nfcii 2423 . . 3
186bnj1317 29170 . . . . . 6
1918nfcii 2423 . . . . 5
2017, 19nfel 2440 . . . 4
2117nfdm 4936 . . . . 5
2221nfeq1 2441 . . . 4
2320, 22nfan 1783 . . 3
24 eleq1 2356 . . . 4
25 dmeq 4895 . . . . 5
2625eqeq1d 2304 . . . 4
2724, 26anbi12d 691 . . 3
2817, 23, 27spcegf 2877 . 2
291, 3, 28sylc 56 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358   w3a 934  wex 1531   wceq 1632   wcel 1696  cab 2282   wne 2459  wral 2556  wrex 2557  crab 2560  cvv 2801  wsbc 3004   cun 3163   wss 3165  c0 3468  csn 3653  cop 3656  cuni 3843   class class class wbr 4039   cdm 4705   cres 4707   wfn 5266  cfv 5271   c-bnj14 29029   w-bnj15 29033   c-bnj18 29035 This theorem is referenced by:  bnj1312  29404 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-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-br 4040  df-opab 4094  df-xp 4711  df-dm 4715  df-res 4717  df-iota 5235  df-fv 5279
 Copyright terms: Public domain W3C validator