Theorem jca2r 16232

Description: Inference conjoining the consequents of two implications.

Hypotheses

Ref	Expression
jca2r.1	|- (ph -> (ps -> ch))
jca2r.2	|- (ps -> th)

Assertion

Ref	Expression
jca2r	|- (ph -> (ps -> (th /\ ch)))

Proof of Theorem jca2r

Step	Hyp	Ref	Expression
1		jca2r.2	. . 3 |- (ps -> th)
2	1	a1i 8	. 2 |- (ph -> (ps -> th))
3		jca2r.1	. 2 |- (ph -> (ps -> ch))
4	2, 3	jcad 661	1 |- (ph -> (ps -> (th /\ ch)))

Syntax hints:   -> wi 3   /\ wa 240

This theorem is referenced by:  prter2 16285

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