Theorem com52l 102

Description: Commutation of antecedents. Rotate left twice. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

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

Assertion

Ref	Expression
com52l	⊢ (𝜒 → (𝜃 → (𝜏 → (𝜑 → (𝜓 → 𝜂)))))

Proof of Theorem com52l

Step	Hyp	Ref	Expression
1		com5.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	com5l 100	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜏 → (𝜑 → 𝜂)))))
3	2	com5l 100	1 ⊢ (𝜒 → (𝜃 → (𝜏 → (𝜑 → (𝜓 → 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:  com52r  103  com5r  104  imp5p  34479