Theorem com35 84

Description: Commutation of antecedents. Swap 3rd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

Ref	Expression
com5.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Assertion

Ref	Expression
com35	⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 𝜂)))))

Proof of Theorem com35

Step	Hyp	Ref	Expression
1		com5.1	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	com34 77	. . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → (𝜏 → 𝜂)))))
3	2	com45 83	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜒 → 𝜂)))))
4	3	com34 77	1 ⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 𝜂)))))

Syntax hints:   → wi 4

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

This theorem is referenced by: (None)