Theorem jctild 314

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

Hypotheses

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

Assertion

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

Proof of Theorem jctild

Step	Hyp	Ref	Expression
1		jctild.2	. . 3 |- ( ph -> th )
2	1	a1d 22	. 2 |- ( ph -> ( ps -> th ) )
3		jctild.1	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	jcad 305	1 |- ( ph -> ( ps -> ( th /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  anc2li  327  syl6an  1422  poxp  6200  ssenen  6817  aptiprleml  7580  zmulcl  9244  rexuz3  10932  cau3lem  11056  gcdzeq  11955  isprm3  12050  epttop  12730  lmtopcnp  12890  txcnp  12911