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Theorem abexex 6783
 Description: A condition where a class builder continues to exist after its wff is existentially quantified. (Contributed by NM, 4-Mar-2007.)
Hypotheses
Ref Expression
abexex.1
abexex.2
abexex.3
Assertion
Ref Expression
abexex
Distinct variable group:   ,,

Proof of Theorem abexex
StepHypRef Expression
1 df-rex 2813 . . . 4
2 abexex.2 . . . . . 6
32pm4.71ri 633 . . . . 5
43exbii 1667 . . . 4
51, 4bitr4i 252 . . 3
65abbii 2591 . 2
7 abexex.1 . . 3
8 abexex.3 . . 3
97, 8abrexex2 6781 . 2
106, 9eqeltrri 2542 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  e.wcel 1818  {cab 2442  E.wrex 2808   cvv 3109 This theorem is referenced by:  brdom7disj  8930  brdom6disj  8931 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-rep 4563  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601
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