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Theorem abrexex2 6781
Description: Existence of an existentially restricted class abstraction. is normally has free-variable parameters and . See also abrexex 6774. (Contributed by NM, 12-Sep-2004.)
Hypotheses
Ref Expression
abrexex2.1
abrexex2.2
Assertion
Ref Expression
abrexex2
Distinct variable group:   , ,

Proof of Theorem abrexex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1707 . . . 4
2 nfcv 2619 . . . . 5
3 nfs1v 2181 . . . . 5
42, 3nfrex 2920 . . . 4
5 sbequ12 1992 . . . . 5
65rexbidv 2968 . . . 4
71, 4, 6cbvab 2598 . . 3
8 df-clab 2443 . . . . 5
98rexbii 2959 . . . 4
109abbii 2591 . . 3
117, 10eqtr4i 2489 . 2
12 df-iun 4332 . . 3
13 abrexex2.1 . . . 4
14 abrexex2.2 . . . 4
1513, 14iunex 6780 . . 3
1612, 15eqeltrri 2542 . 2
1711, 16eqeltri 2541 1
Colors of variables: wff setvar class
Syntax hints:  [wsb 1739  e.wcel 1818  {cab 2442  E.wrex 2808   cvv 3109  U_ciun 4330
This theorem is referenced by:  abexssex  6782  abexex  6783  oprabrexex2  6790  ab2rexex  6791  ab2rexex2  6792
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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