Theorem mpdd 47

Description: A nested modus ponens deduction.

Hypotheses

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

Assertion

Ref	Expression
mpdd	|- (ph -> (ps -> th))

Proof of Theorem mpdd

Step	Hyp	Ref	Expression
1		mpdd.1	. 2 |- (ph -> (ps -> ch))
2		mpdd.2	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	a2d 15	. 2 |- (ph -> ((ps -> ch) -> (ps -> th)))
4	1, 3	mpd 46	1 |- (ph -> (ps -> th))

Syntax hints:   -> wi 2

This theorem is referenced by:  mpid 48  syldd 50  oaordex 3160  oaass 3163  omordi 3164  nnmord 3189  brecop 3242  sumdmdlem 5786

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

metamath.org