Theorem jaao 427

Description: Inference conjoining and disjoining the antecedents of two implications.

Hypotheses

Ref	Expression
jaao.1	|- (ph -> (ps -> ch))
jaao.2	|- (th -> (ta -> ch))

Assertion

Ref	Expression
jaao	|- ((ph /\ th) -> ((ps \/ ta) -> ch))

Proof of Theorem jaao

Step	Hyp	Ref	Expression
1		jaao.1	. . 3 |- (ph -> (ps -> ch))
2	1	adantr 389	. 2 |- ((ph /\ th) -> (ps -> ch))
3		jaao.2	. . 3 |- (th -> (ta -> ch))
4	3	adantl 388	. 2 |- ((ph /\ th) -> (ta -> ch))
5	2, 4	jaod 424	1 |- ((ph /\ th) -> ((ps \/ ta) -> ch))

Syntax hints:   -> wi 3   \/ wo 222   /\ wa 223

This theorem is referenced by:  prss 2467  fr2nr 2920  ordtri1 2975  ordun 3076  suc11 3088  funun 3546  suc11reg 4585  abslt 6818  absle 6819  absltOLD 6820  absleOLD 6821  unctb 7527

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

Copyright terms: Public domain