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Theorem ifel 3697
Description: Membership of a conditional operator. (Contributed by NM, 10-Sep-2005.)
Assertion
Ref Expression
ifel

Proof of Theorem ifel
StepHypRef Expression
1 eleq1 2413 . 2
2 eleq1 2413 . 2
31, 2elimif 3691 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wb 176   wo 357   wa 358   wcel 1710  cif 3662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663
This theorem is referenced by: (None)
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