Theorem pm5.75 937

Description: Theorem *5.75 of [WhiteheadRussell] p. 126. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 23-Dec-2012.)

Assertion

Ref	Expression
pm5.75

Proof of Theorem pm5.75

Step	Hyp	Ref	Expression
1		anbi1 706	. . 3
2		orcom 387	. . . . 5
3	2	anbi1i 695	. . . 4
4		pm5.61 712	. . . 4
5	3, 4	bitri 249	. . 3
6	1, 5	syl6bb 261	. 2
7		pm4.71 630	. . . 4
8	7	biimpi 194	. . 3
9	8	bicomd 201	. 2
10	6, 9	sylan9bbr 700	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371