Theorem a1ddd 80

Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd 50. Double deduction associated with a1d 25. Triple deduction associated with ax-1 6 and a1i 11. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1ddd.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Assertion

Ref	Expression
a1ddd	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem a1ddd

Step	Hyp	Ref	Expression
1		a1ddd.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
2		ax-1 6	. 2 ⊢ (𝜏 → (𝜃 → 𝜏))
3	1, 2	syl8 76	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4

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

This theorem is referenced by:  tfindsg  7707  findsg  7746  difreicc  13216  swrdswrdlem  14417