Theorem pm2.82 725

Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.82	|- ( ( ( ph \/ ps ) \/ ch ) -> ( ( ( ph \/ -. ch ) \/ th ) -> ( ( ph \/ ps ) \/ th ) ) )

Proof of Theorem pm2.82

Step	Hyp	Ref	Expression
1		ax-1 5	. . 3 |- ( ( ph \/ ps ) -> ( ( ph \/ -. ch ) -> ( ph \/ ps ) ) )
2		pm2.24 551	. . . 4 |- ( ch -> ( -. ch -> ps ) )
3	2	orim2d 702	. . 3 |- ( ch -> ( ( ph \/ -. ch ) -> ( ph \/ ps ) ) )
4	1, 3	jaoi 636	. 2 |- ( ( ( ph \/ ps ) \/ ch ) -> ( ( ph \/ -. ch ) -> ( ph \/ ps ) ) )
5	4	orim1d 701	1 |- ( ( ( ph \/ ps ) \/ ch ) -> ( ( ( ph \/ -. ch ) \/ th ) -> ( ( ph \/ ps ) \/ th ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)