Theorem pm2.64 747

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 5	. . 3 |- ( ph -> ( ( ph \/ ps ) -> ph ) )
2		orel2 677	. . 3 |- ( -. ps -> ( ( ph \/ ps ) -> ph ) )
3	1, 2	jaoi 668	. 2 |- ( ( ph \/ -. ps ) -> ( ( ph \/ ps ) -> ph ) )
4	3	com12 30	1 |- ( ( ph \/ ps ) -> ( ( ph \/ -. ps ) -> ph ) )

Syntax hints:   -. wn 3   -> wi 4   \/ 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: (None)