Theorem mpdi 38

Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.)

Hypotheses

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

Assertion

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

Proof of Theorem mpdi

Step	Hyp	Ref	Expression
1		mpdi.1	. . 3 |- (ps -> ch)
2	1	a1i 10	. 2 |- (ph -> (ps -> ch))
3		mpdi.2	. 2 |- (ph -> (ps -> (ch -> th)))
4	2, 3	mpdd 36	1 |- (ph -> (ps -> 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:  mpii  39  pm2.43d  44  impt  149  enpw1  6063