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Theorem bnj1124 29294
 Description: Property of . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1124.4
bnj1124.5
Assertion
Ref Expression
bnj1124

Proof of Theorem bnj1124
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 biid 228 . 2
2 biid 228 . 2
3 biid 228 . 2
4 bnj1124.4 . 2
5 bnj1124.5 . 2
6 biid 228 . 2
7 eqid 2435 . 2
8 eqid 2435 . 2
9 biid 228 . 2
10 biid 228 . 2
11 biid 228 . 2
12 biid 228 . 2
13 biid 228 . 2
14 biid 228 . 2
15 biid 228 . 2
16 biid 228 . 2
17 biid 228 . 2
18 biid 228 . 2
19 biid 228 . 2
201, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19bnj1030 29293 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  cab 2421  wral 2697  wrex 2698  cvv 2948  wsbc 3153   cdif 3309   wss 3312  c0 3620  csn 3806  ciun 4085   class class class wbr 4204   cep 4484   csuc 4575  com 4837   cdm 4870   wfn 5441  cfv 5446   w-bnj17 28987   c-bnj14 28989   w-bnj15 28993   c-bnj18 28995   w-bnj19 28997 This theorem is referenced by:  bnj1125  29298  bnj1136  29303  bnj1408  29342 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-tr 4295  df-eprel 4486  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-suc 4579  df-om 4838  df-iota 5410  df-fn 5449  df-fv 5454  df-bnj17 28988  df-bnj18 28996  df-bnj19 28998
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