Theorem a1ddd

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

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

Proof

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