Theorem 2a1dd 51

Description: Double deduction introducing two antecedents. Two applications of 2a1dd 51. Deduction associated with 2a1d 26. Double deduction associated with 2a1 28 and 2a1i 12. (Contributed by Jeff Hankins, 5-Aug-2009.)

Hypothesis

Ref	Expression
2a1dd.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
2a1dd	⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → 𝜒))))

Proof of Theorem 2a1dd

Step	Hyp	Ref	Expression
1		2a1dd.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	a1dd 50	. 2 ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜒)))
3	2	a1dd 50	1 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → 𝜒))))

Syntax hints:   → wi 4

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

This theorem is referenced by:  nnsub  12017