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Metamath Proof Explorer

Theorem a1dd

Description: Double deduction introducing an antecedent. Deduction associated with a1d . Double deduction associated with ax-1 and a1i . (Contributed by NM, 17-Dec-2004) (Proof shortened by Mel L. O'Cat, 15-Jan-2008)

		Ref	Expression
	Hypothesis	a1dd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	Assertion	a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		a1dd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ax-1	⊢ ( 𝜒 → ( 𝜃 → 𝜒 ) )
3	1 2	syl6	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )