Theorem ifpr 4077

Description: Membership of a conditional operator in an unordered pair. (Contributed by NM, 17-Jun-2007.)

Assertion

Ref	Expression
ifpr

Proof of Theorem ifpr

Step	Hyp	Ref	Expression
1		elex 3118	. 2
2		elex 3118	. 2
3		ifcl 3983	. . 3
4		ifeqor 3985	. . . 4
5		elprg 4045	. . . 4
6	4, 5	mpbiri 233	. . 3
7	3, 6	syl 16	. 2
8	1, 2, 7	syl2an 477	1

Syntax hints:  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  cvv 3109  ifcif 3941  {cpr 4031

This theorem is referenced by:  suppr  7950  uvcvvcl  18818  indf  28029

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-if 3942  df-sn 4030  df-pr 4032