Theorem com35 99

Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 96. Double deduction associated with com13 89. (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 92	. . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → (𝜏 → 𝜂)))))
3	2	com45 98	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜒 → 𝜂)))))
4	3	com34 92	1 ⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 𝜂)))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  swrdswrdlem  14765  bcthlem5  25540  nocvxminlem  28000  satffunlem  35932  iccpartigtl  48232  grimuhgr  48712  nn0sumshdiglemB  49459