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Theorem ifpr 3585
 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 2735 . 2
2 elex 2735 . 2
3 ifcl 3506 . . 3
4 ifeqor 3507 . . . 4
5 elprg 3561 . . . 4
64, 5mpbiri 226 . . 3
73, 6syl 17 . 2
81, 2, 7syl2an 465 1
 Colors of variables: wff set class Syntax hints:   wi 6   wo 359   wa 360   wceq 1619   wcel 1621  cvv 2727  cif 3470  cpr 3545 This theorem is referenced by:  suppr  7103  uvcvvcl  26402 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-if 3471  df-sn 3550  df-pr 3551
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