Theorem pm2.64 791

Description: Theorem *2.64 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.64	|- ( ( ph \/ ps ) -> ( ( ph \/ -. ps ) -> ph ) )

Proof of Theorem pm2.64

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- ( ph -> ( ( ph \/ ps ) -> ph ) )
2		orel2 716	. . 3 |- ( -. ps -> ( ( ph \/ ps ) -> ph ) )
3	1, 2	jaoi 706	. 2 |- ( ( ph \/ -. ps ) -> ( ( ph \/ ps ) -> ph ) )
4	3	com12 30	1 |- ( ( ph \/ ps ) -> ( ( ph \/ -. ps ) -> ph ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)