Theorem ab2rexex 6791

Description: Existence of a class abstraction of existentially restricted sets. Variables and are normally free-variable parameters in the class expression substituted for , which can be thought of as (x,). See comments for abrexex 6774. (Contributed by NM, 20-Sep-2011.)

Hypotheses

Ref	Expression
ab2rexex.1
ab2rexex.2

Assertion

Ref	Expression
ab2rexex

Distinct variable groups:   ,,   ,,   ,

Proof of Theorem ab2rexex

Step	Hyp	Ref	Expression
1		ab2rexex.1	. 2
2		ab2rexex.2	. . 3
3	2	abrexex 6774	. 2
4	1, 3	abrexex2 6781	1

Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808  cvv 3109

This theorem is referenced by:  plyval  22590  pstmfval  27875  pstmxmet  27876

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