Theorem pm3.44 497

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		id 19	. 2 |- ((ps -> ph) -> (ps -> ph))
2		id 19	. 2 |- ((ch -> ph) -> (ch -> ph))
3	1, 2	jaao 495	1 |- (((ps -> ph) /\ (ch -> ph)) -> ((ps \/ ch) -> ph))

Syntax hints:   -> wi 4   \/ wo 357   /\ wa 358

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 177  df-or 359  df-an 360

This theorem is referenced by:  jao  498  jaob  758