Theorem com25 85

Description: Commutation of antecedents. Swap 2nd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

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

Assertion

Ref	Expression
com25	⊢ (φ → (τ → (χ → (θ → (ψ → η)))))

Proof of Theorem com25

Step	Hyp	Ref	Expression
1		com5.1	. . . 4 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2	1	com24 81	. . 3 ⊢ (φ → (θ → (χ → (ψ → (τ → η)))))
3	2	com45 83	. 2 ⊢ (φ → (θ → (χ → (τ → (ψ → η)))))
4	3	com24 81	1 ⊢ (φ → (τ → (χ → (θ → (ψ → 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: (None)