Theorem eqif 3979

Description: Expansion of an equality with a conditional operator. (Contributed by NM, 14-Feb-2005.)

Assertion

Ref	Expression
eqif

Proof of Theorem eqif

Step	Hyp	Ref	Expression
1		eqeq2 2472	. 2
2		eqeq2 2472	. 2
3	1, 2	elimif 3975	1

Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  ifcif 3941

This theorem is referenced by:  ifval  3980  xpima  5454  fin23lem19  8737  fin23lem28  8741  fin23lem29  8742  fin23lem30  8743  aalioulem3  22730  ifbieq12d2  27420  iocinif  27592  fsumcvg4  27932  ind1a  28034  esumsn  28072  itg2addnclem2  30067  afvpcfv0  32231

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