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Theorem ee30 37993
Description: e30 37992 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee30.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee30.2 𝜏
ee30.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
ee30 (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee30
StepHypRef Expression
1 ee30.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee30.2 . . . . 5 𝜏
32a1i 11 . . . 4 (𝜒𝜏)
43a1i 11 . . 3 (𝜓 → (𝜒𝜏))
54a1i 11 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
6 ee30.3 . 2 (𝜃 → (𝜏𝜂))
71, 5, 6ee33 37748 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:  ee30an  37995
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