Theorem com5l 86

Description: Commutation of antecedents. Rotate left. (Contributed by Jeff Hankins, 28-Jun-2009.) (Proof shortened by Wolf Lammen, 29-Jul-2012.)

Hypothesis

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

Assertion

Ref	Expression
com5l	⊢ (ψ → (χ → (θ → (τ → (φ → η)))))

Proof of Theorem com5l

Step	Hyp	Ref	Expression
1		com5.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2	1	com4l 78	. 2 ⊢ (ψ → (χ → (θ → (φ → (τ → η)))))
3	2	com45 83	1 ⊢ (ψ → (χ → (θ → (τ → (φ → 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:  com15  87  com52l  88  com52r  89