Theorem pm4.79 607

Description: Theorem *4.79 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 27-Jun-2013.)

Assertion

Ref	Expression
pm4.79	|- ( ( ( ps -> ph ) \/ ( ch -> ph ) ) <-> ( ( ps /\ ch ) -> ph ) )

Proof of Theorem pm4.79

Step	Hyp	Ref	Expression
1		id 22	. . 3 |- ( ( ps -> ph ) -> ( ps -> ph ) )
2		id 22	. . 3 |- ( ( ch -> ph ) -> ( ch -> ph ) )
3	1, 2	jaoa 532	. 2 |- ( ( ( ps -> ph ) \/ ( ch -> ph ) ) -> ( ( ps /\ ch ) -> ph ) )
4		simplim 163	. . . 4 |- ( -. ( ps -> ph ) -> ps )
5		pm3.3 460	. . . 4 |- ( ( ( ps /\ ch ) -> ph ) -> ( ps -> ( ch -> ph ) ) )
6	4, 5	syl5 34	. . 3 |- ( ( ( ps /\ ch ) -> ph ) -> ( -. ( ps -> ph ) -> ( ch -> ph ) ) )
7	6	orrd 393	. 2 |- ( ( ( ps /\ ch ) -> ph ) -> ( ( ps -> ph ) \/ ( ch -> ph ) ) )
8	3, 7	impbii 199	1 |- ( ( ( ps -> ph ) \/ ( ch -> ph ) ) <-> ( ( ps /\ ch ) -> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

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:  islinindfis  42238