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Theorem com35 98
Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 95. Double deduction associated with com13 88. (Contributed by Jeff Hankins, 28-Jun-2009.)
Hypothesis
Ref Expression
com5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
com35 (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒𝜂)))))

Proof of Theorem com35
StepHypRef Expression
1 com5.1 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21com34 91 . . 3 (𝜑 → (𝜓 → (𝜃 → (𝜒 → (𝜏𝜂)))))
32com45 97 . 2 (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜒𝜂)))))
43com34 91 1 (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  swrdswrdlem  13659  bcthlem5  23325  nocvxminlem  32199  iccpartigtl  41869  nn0sumshdiglemB  42924
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