Theorem jctild 316

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

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:  anc2li  329  syl6an  1445  poxp  6290  ssenen  6912  aptiprleml  7706  zmulcl  9379  rexuz3  11155  cau3lem  11279  gcdzeq  12189  isprm3  12286  epttop  14326  lmtopcnp  14486  txcnp  14507