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Theorem com25 89
Description: Commutation of antecedents. Swap 2nd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)
Hypothesis
Ref Expression
com5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
com25 (𝜑 → (𝜏 → (𝜒 → (𝜃 → (𝜓𝜂)))))

Proof of Theorem com25
StepHypRef Expression
1 com5.1 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21com24 85 . . 3 (𝜑 → (𝜃 → (𝜒 → (𝜓 → (𝜏𝜂)))))
32com45 87 . 2 (𝜑 → (𝜃 → (𝜒 → (𝜏 → (𝜓𝜂)))))
43com24 85 1 (𝜑 → (𝜏 → (𝜒 → (𝜃 → (𝜓𝜂)))))
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:  bj-inf2vnlem2  10483
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