Theorem jca2 16231

Description: Inference conjoining the consequents of two implications.

Hypotheses

Ref	Expression
jca2.1	|- (ph -> (ps -> ch))
jca2.2	|- (ps -> th)

Assertion

Ref	Expression
jca2	|- (ph -> (ps -> (ch /\ th)))

Proof of Theorem jca2

Step	Hyp	Ref	Expression
1		jca2.1	. 2 |- (ph -> (ps -> ch))
2		jca2.2	. . 3 |- (ps -> th)
3	2	a1i 8	. 2 |- (ph -> (ps -> th))
4	1, 3	jcad 661	1 |- (ph -> (ps -> (ch /\ th)))

Syntax hints:   -> wi 3   /\ wa 240

This theorem is referenced by:  jca3 16233

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