Theorem syl6com 31

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005.)

Hypotheses

Ref	Expression
syl6com.1	⊢ (φ → (ψ → χ))
syl6com.2	⊢ (χ → θ)

Assertion

Ref	Expression
syl6com	⊢ (ψ → (φ → θ))

Proof of Theorem syl6com

Step	Hyp	Ref	Expression
1		syl6com.1	. . 3 ⊢ (φ → (ψ → χ))
2		syl6com.2	. . 3 ⊢ (χ → θ)
3	1, 2	syl6 29	. 2 ⊢ (φ → (ψ → θ))
4	3	com12 27	1 ⊢ (ψ → (φ → θ))

Syntax hints:   → wi 4

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

This theorem is referenced by:  19.33b  1608  ax9  1949  ax16i  2046  ax16ALT2  2048  funcnvuni  5162  nchoicelem17  6306