Theorem jca3 16233

Description: Inference conjoining the consequents of two implications.

Hypotheses

Ref	Expression
jca3.1	|- (ph -> (ps -> ch))
jca3.2	|- (th -> ta)

Assertion

Ref	Expression
jca3	|- (ph -> (ps -> (th -> (ch /\ ta))))

Proof of Theorem jca3

Step	Hyp	Ref	Expression
1		jca3.1	. . . . 5 |- (ph -> (ps -> ch))
2	1	imp 377	. . . 4 |- ((ph /\ ps) -> ch)
3	2	a1d 15	. . 3 |- ((ph /\ ps) -> (th -> ch))
4		jca3.2	. . 3 |- (th -> ta)
5	3, 4	jca2 16231	. 2 |- ((ph /\ ps) -> (th -> (ch /\ ta)))
6	5	ex 402	1 |- (ph -> (ps -> (th -> (ch /\ ta))))

Syntax hints:   -> wi 3   /\ wa 240

This theorem is referenced by:  prtlem10 16265

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 164  df-an 242

Copyright terms: Public domain