Theorem 2a1dd

Description: Double deduction introducing two antecedents. Two applications of 2a1dd . Deduction associated with 2a1d . Double deduction associated with 2a1 and 2a1i . (Contributed by Jeff Hankins, 5-Aug-2009)

	Ref	Expression
Hypothesis	2a1dd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	2a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜒 ) ) ) )

Proof

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