Theorem embantd 50

Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)

Hypotheses

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

Assertion

Ref	Expression
embantd	|- (ph -> ((ps -> ch) -> th))

Proof of Theorem embantd

Step	Hyp	Ref	Expression
1		embantd.1	. 2 |- (ph -> ps)
2		embantd.2	. . 3 |- (ph -> (ch -> th))
3	2	imim2d 48	. 2 |- (ph -> ((ps -> ch) -> (ps -> th)))
4	1, 3	mpid 37	1 |- (ph -> ((ps -> ch) -> th))

Syntax hints:   -> wi 4

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

This theorem is referenced by:  spimt  1974  ltfintri  4467  evenoddnnnul  4515  evenodddisj  4517  nnadjoin  4521  sfintfin  4533  tfinnn  4535  nchoicelem17  6306