Theorem com15 87

Description: Commutation of antecedents. Swap 1st and 5th. (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
com15	⊢ (τ → (ψ → (χ → (θ → (φ → η)))))

Proof of Theorem com15

Step	Hyp	Ref	Expression
1		com5.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2	1	com5l 86	. 2 ⊢ (ψ → (χ → (θ → (τ → (φ → η)))))
3	2	com4r 80	1 ⊢ (τ → (ψ → (χ → (θ → (φ → 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: (None)