Theorem com24 81

Description: Commutation of antecedents. Swap 2nd and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com4.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
com24	⊢ (φ → (θ → (χ → (ψ → τ))))

Proof of Theorem com24

Step	Hyp	Ref	Expression
1		com4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	com4t 79	. 2 ⊢ (χ → (θ → (φ → (ψ → τ))))
3	2	com13 74	1 ⊢ (φ → (θ → (χ → (ψ → τ))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com25  85  nclenn  6250