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Theorem ifpr 3880
 Description: Membership of a conditional operator in an unordered pair. (Contributed by NM, 17-Jun-2007.)
Assertion
Ref Expression
ifpr

Proof of Theorem ifpr
StepHypRef Expression
1 elex 2970 . 2
2 elex 2970 . 2
3 ifcl 3799 . . 3
4 ifeqor 3800 . . . 4
5 elprg 3855 . . . 4
64, 5mpbiri 226 . . 3
73, 6syl 16 . 2
81, 2, 7syl2an 465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   wceq 1653   wcel 1727  cvv 2962  cif 3763  cpr 3839 This theorem is referenced by:  suppr  7502  indf  24444  uvcvvcl  27251 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2964  df-un 3311  df-if 3764  df-sn 3844  df-pr 3845
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