Theorem com35 96

Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 93. (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 89	. . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → (𝜏 → 𝜂)))))
3	2	com45 95	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜒 → 𝜂)))))
4	3	com34 89	1 ⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 𝜂)))))

Syntax hints:   → wi 4

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

This theorem is referenced by:  swrdswrdlem  13311  bcthlem5  22933  3v3e3cycl1  26172  4cycl4v4e  26194  4cycl4dv4e  26196  nocvxminlem  31089  iccpartigtl  39961  nn0sumshdiglemB  42212