Theorem pm5.74 244

Description: Distribution of implication over biconditional. Theorem *5.74 of [WhiteheadRussell] p. 126. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 11-Apr-2013.)

Assertion

Ref	Expression
pm5.74

Proof of Theorem pm5.74

Step	Hyp	Ref	Expression
1		bi1 186	. . . 4
2	1	imim3i 59	. . 3
3		bi2 198	. . . 4
4	3	imim3i 59	. . 3
5	2, 4	impbid 191	. 2
6		bi1 186	. . . 4
7	6	pm2.86d 99	. . 3
8		bi2 198	. . . 4
9	8	pm2.86d 99	. . 3
10	7, 9	impbidd 189	. 2
11	5, 10	impbii 188	1

Syntax hints:  ->wi 4  <->wb 184

This theorem is referenced by:  pm5.74i  245  pm5.74ri  246  pm5.74d  247  pm5.74rd  248  bibi2d  318  pm5.32  636  orbidi  932

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