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Theorem imp5aOLD 440
Description: Obsolete version of imp5a 429 as of 2-Aug-2022. (Contributed by Jeff Hankins, 7-Jul-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
imp5aOLD.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5aOLD (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))

Proof of Theorem imp5aOLD
StepHypRef Expression
1 imp5aOLD.1 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
2 pm3.31 438 . 2 ((𝜃 → (𝜏𝜂)) → ((𝜃𝜏) → 𝜂))
31, 2syl8 76 1 (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 198  df-an 385
This theorem is referenced by: (None)
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