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Theorem syl6com 35
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 33 . 2 (𝜑 → (𝜓𝜃))
43com12 30 1 (𝜓 → (𝜑𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  pclem6  1281  spimh  1641  ax16  1710  ax16i  1754  elres  4674  funcnvuni  4996  funrnex  5769  bj-inf2vnlem2  10483
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