Theorem elimif 3975

Description: Elimination of a conditional operator contained in a wff . (Contributed by NM, 15-Feb-2005.) (Proof shortened by NM, 25-Apr-2019.)

Hypotheses

Ref	Expression
elimif.1
elimif.2

Assertion

Ref	Expression
elimif

Proof of Theorem elimif

Step	Hyp	Ref	Expression
1		iftrue 3947	. . 3
2		elimif.1	. . 3
3	1, 2	syl 16	. 2
4		iffalse 3950	. . 3
5		elimif.2	. . 3
6	4, 5	syl 16	. 2
7	3, 6	cases 970	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  ifcif 3941

This theorem is referenced by:  eqif  3979  elif  3981  ifel  3982  ftc1anclem5  30094

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