Theorem mpdi 48

Description: A nested modus ponens deduction. (The proof was 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 8	. 2 |- (ph -> (ps -> ch))
3		mpdi.2	. 2 |- (ph -> (ps -> (ch -> th)))
4	2, 3	mpdd 46	1 |- (ph -> (ps -> th))

Syntax hints:   -> wi 3

This theorem is referenced by:  fvopab2 3776  tfrlem9 3904  mulcmpblnr 5155  metcn4i 7906

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

Copyright terms: Public domain