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Metamath Proof Explorer

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	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
	Assertion	a1ddd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

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