Theorem ifnot 3986

Description: Negating the first argument swaps the last two arguments of a conditional operator. (Contributed by NM, 21-Jun-2007.)

Assertion

Ref	Expression
ifnot

Proof of Theorem ifnot

Step	Hyp	Ref	Expression
1		notnot1 122	. . . 4
2	1	iffalsed 3952	. . 3
3		iftrue 3947	. . 3
4	2, 3	eqtr4d 2501	. 2
5		iftrue 3947	. . 3
6		iffalse 3950	. . 3
7	5, 6	eqtr4d 2501	. 2
8	4, 7	pm2.61i 164	1

Syntax hints:  -.wn 3  =wceq 1395  ifcif 3941

This theorem is referenced by:  suppsnop  6932  sadadd2lem2  14100  maducoeval2  19142  tmsxpsval2  21042  itg2uba  22150  lgsneg  23594  lgsdilem  23597  sgnneg  28479  itgaddnclem2  30074  ftc1anclem5  30094  bj-xpimasn  34512

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