Theorem ifel 3982

Description: Membership of a conditional operator. (Contributed by NM, 10-Sep-2005.)

Assertion

Ref	Expression
ifel

Proof of Theorem ifel

Step	Hyp	Ref	Expression
1		eleq1 2529	. 2
2		eleq1 2529	. 2
3	1, 2	elimif 3975	1

Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  e.wcel 1818  ifcif 3941

This theorem is referenced by:  clwlkisclwwlklem2a  24785

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-if 3942