Theorem jctird 317

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 307	1 |- ( ph -> ( ps -> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  anc2ri  330  ordunisuc2r  4550  fnun  5364  fco  5423  fiintim  6992  cauappcvgprlemladdru  7723  cauappcvgprlemladdrl  7724  caucvgprlemnkj  7733  dvdsdivcl  12015  cnrest2  14472  cnptopresti  14474  bdxmet  14737  lgsdir  15276