Theorem a1ddd 1456

Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd 48. Double deduction associated with a1d 22. Triple deduction associated with ax-1 6 and a1i 9. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1ddd.1	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Assertion

Ref	Expression
a1ddd	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem a1ddd

Step	Hyp	Ref	Expression
1		a1ddd.1	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
2		ax-1 6	. 2 |- ( ta -> ( th -> ta ) )
3	1, 2	syl8 71	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  swrdswrdlem  11163