Theorem pm3.44 715

Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Assertion

Ref	Expression
pm3.44	|- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Proof of Theorem pm3.44

Step	Hyp	Ref	Expression
1		jaob 710	. 2 |- ( ( ( ps \/ ch ) -> ph ) <-> ( ( ps -> ph ) /\ ( ch -> ph ) ) )
2	1	biimpri 133	1 |- ( ( ( ps -> ph ) /\ ( ch -> ph ) ) -> ( ( ps \/ ch ) -> ph ) )

Syntax hints:   -> wi 4   /\ wa 104   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  jaoi  716  jao  755  pm2.6dc  862  pm4.83dc  951