Theorem jctild 527

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 519	1 |- (ph -> (ps -> (th /\ ch)))

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:  anc2li  540  ee12an  1363  ax12olem1  1927  2eu1  2284  xpcan  5058  xpcan2  5059