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Theorem ifcl 3698
Description: Membership (closure) of a conditional operator. (Contributed by NM, 4-Apr-2005.)
Assertion
Ref Expression
ifcl

Proof of Theorem ifcl
StepHypRef Expression
1 eleq1 2413 . 2
2 eleq1 2413 . 2
31, 2ifboth 3693 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   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:  ifpr  3774
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