Theorem ifeqor 3985

Description: The possible values of a conditional operator. (Contributed by NM, 17-Jun-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Assertion

Ref	Expression
ifeqor

Proof of Theorem ifeqor

Step	Hyp	Ref	Expression
1		iftrue 3947	. . . 4
2	1	con3i 135	. . 3
3	2	iffalsed 3952	. 2
4	3	orri 376	1

Syntax hints:  -.wn 3  \/wo 368  =wceq 1395  ifcif 3941

This theorem is referenced by:  ifpr  4077  rabrsn  4100  muval2  23408

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