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Theorem ee31 42396
Description: e31 42395 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee31.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee31.2 (𝜑𝜏)
ee31.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
ee31 (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee31
StepHypRef Expression
1 ee31.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee31.2 . . . 4 (𝜑𝜏)
32a1d 25 . . 3 (𝜑 → (𝜒𝜏))
43a1d 25 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
5 ee31.3 . 2 (𝜃 → (𝜏𝜂))
61, 4, 5ee33 42165 1 (𝜑 → (𝜓 → (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:  trintALT  42525
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