Theorem pm2.74 891

Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm2.74	|- ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		orel2 398	. . 3 |- ( -. ps -> ( ( ph \/ ps ) -> ph ) )
2		ax-1 6	. . 3 |- ( ph -> ( ( ph \/ ps ) -> ph ) )
3	1, 2	ja 173	. 2 |- ( ( ps -> ph ) -> ( ( ph \/ ps ) -> ph ) )
4	3	orim1d 884	1 |- ( ( ps -> ph ) -> ( ( ( ph \/ ps ) \/ ch ) -> ( ph \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 383

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 197  df-or 385  df-an 386

This theorem is referenced by: (None)