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Theorem 3com12d 32632
Description: Commutation in consequent. Swap 1st and 2nd. (Contributed by Jeff Hankins, 17-Nov-2009.)
Hypothesis
Ref Expression
3com12d.1 (𝜑 → (𝜓𝜒𝜃))
Assertion
Ref Expression
3com12d (𝜑 → (𝜒𝜓𝜃))

Proof of Theorem 3com12d
StepHypRef Expression
1 3com12d.1 . 2 (𝜑 → (𝜓𝜒𝜃))
2 id 22 . . 3 ((𝜒𝜓𝜃) → (𝜒𝜓𝜃))
323com12 1118 . 2 ((𝜓𝜒𝜃) → (𝜒𝜓𝜃))
41, 3syl 17 1 (𝜑 → (𝜒𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 385  df-3an 1074
This theorem is referenced by: (None)
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