Theorem pm5.61 740

Description: Theorem *5.61 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 30-Jun-2013.)

Assertion

Ref	Expression
pm5.61	|- ( ( ( ph \/ ps ) /\ -. ps ) <-> ( ph /\ -. ps ) )

Proof of Theorem pm5.61

Step	Hyp	Ref	Expression
1		biorf 695	. . 3 |- ( -. ps -> ( ph <-> ( ps \/ ph ) ) )
2		orcom 679	. . 3 |- ( ( ps \/ ph ) <-> ( ph \/ ps ) )
3	1, 2	syl6rbb 195	. 2 |- ( -. ps -> ( ( ph \/ ps ) <-> ph ) )
4	3	pm5.32ri 442	1 |- ( ( ( ph \/ ps ) /\ -. ps ) <-> ( ph /\ -. ps ) )

Syntax hints:   -. wn 3   /\ wa 102   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm5.75  903  excxor  1309  xrnemnf  8853  xrnepnf  8854