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Theorem syl6com 31
Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005.)
Hypotheses
Ref Expression
syl6com.1 (φ → (ψχ))
syl6com.2 (χθ)
Assertion
Ref Expression
syl6com (ψ → (φθ))

Proof of Theorem syl6com
StepHypRef Expression
1 syl6com.1 . . 3 (φ → (ψχ))
2 syl6com.2 . . 3 (χθ)
31, 2syl6 29 . 2 (φ → (ψθ))
43com12 27 1 (ψ → (φθ))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
This theorem is referenced by:  19.33b  1608  ax9  1949  ax16i  2046  ax16ALT2  2048  funcnvuni  5161  nchoicelem17  6305
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