Theorem ifcomnan 3990

Description: Commute the conditions in two nested conditionals if both conditions are not simultaneously true. (Contributed by SO, 15-Jul-2018.)

Assertion

Ref	Expression
ifcomnan

Proof of Theorem ifcomnan

Step	Hyp	Ref	Expression
1		pm3.13 501	. 2
2		iffalse 3950	. . . 4
3		iffalse 3950	. . . . 5
4	3	ifeq2d 3960	. . . 4
5	2, 4	eqtr4d 2501	. . 3
6		iffalse 3950	. . . . 5
7	6	ifeq2d 3960	. . . 4
8		iffalse 3950	. . . 4
9	7, 8	eqtr4d 2501	. . 3
10	5, 9	jaoi 379	. 2
11	1, 10	syl 16	1

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

This theorem is referenced by:  mdetunilem6  19119

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-nfc 2607  df-rab 2816  df-v 3111  df-un 3480  df-if 3942