Theorem imp5p 34500

Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Hypothesis

Ref	Expression
3imp5.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Assertion

Ref	Expression
imp5p	⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜂)))

Proof of Theorem imp5p

Step	Hyp	Ref	Expression
1		3imp5.1	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	com52l 102	. . 3 ⊢ (𝜒 → (𝜃 → (𝜏 → (𝜑 → (𝜓 → 𝜂)))))
3	2	3imp 1110	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → (𝜑 → (𝜓 → 𝜂)))
4	3	com3l 89	1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜂)))

Syntax hints:   → wi 4   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088

This theorem is referenced by: (None)