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Theorem ee022 41272
Description: e022 41271 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee022.1 𝜑
ee022.2 (𝜓 → (𝜒𝜃))
ee022.3 (𝜓 → (𝜒𝜏))
ee022.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee022 (𝜓 → (𝜒𝜂))

Proof of Theorem ee022
StepHypRef Expression
1 ee022.1 . . . 4 𝜑
21a1i 11 . . 3 (𝜒𝜑)
32a1i 11 . 2 (𝜓 → (𝜒𝜑))
4 ee022.2 . 2 (𝜓 → (𝜒𝜃))
5 ee022.3 . 2 (𝜓 → (𝜒𝜏))
6 ee022.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
73, 4, 5, 6ee222 41132 1 (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  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400
This theorem is referenced by: (None)
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