Theorem jctird 528

Description: Deduction conjoining a theorem to right of consequent in an implication. (Contributed by NM, 21-Apr-2005.)

Hypotheses

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

Assertion

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

Proof of Theorem jctird

Step	Hyp	Ref	Expression
1		jctird.1	. 2 |- (ph -> (ps -> ch))
2		jctird.2	. . 3 |- (ph -> th)
3	2	a1d 22	. 2 |- (ph -> (ps -> th))
4	1, 3	jcad 519	1 |- (ph -> (ps -> (ch /\ th)))

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  anc2ri  541  fnun  5190  fco  5232