Theorem com13 74

Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com3.1	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
com13	⊢ (χ → (ψ → (φ → θ)))

Proof of Theorem com13

Step	Hyp	Ref	Expression
1		com3.1	. . 3 ⊢ (φ → (ψ → (χ → θ)))
2	1	com3r 73	. 2 ⊢ (χ → (φ → (ψ → θ)))
3	2	com23 72	1 ⊢ (χ → (ψ → (φ → θ)))

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:  com24  81  an13s  778  an31s  781  meredith  1404