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Theorem com45 97
 Description: Commutation of antecedents. Swap 4th and 5th. Deduction associated with com34 91. Double deduction associated with com23 86. Triple deduction associated with com12 32. (Contributed by Jeff Hankins, 28-Jun-2009.)
Hypothesis
Ref Expression
com5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
com45 (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂)))))

Proof of Theorem com45
StepHypRef Expression
1 com5.1 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
2 pm2.04 90 . 2 ((𝜃 → (𝜏𝜂)) → (𝜏 → (𝜃𝜂)))
31, 2syl8 76 1 (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂)))))
 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:  com35  98  com25  99  com5l  100  lcmfdvdsb  15821  prmgaplem6  16226  islmhm2  19505  dfon2lem8  32649
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