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Theorem ee212 41282
Description: e212 41281 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee212.1 (𝜑 → (𝜓𝜒))
ee212.2 (𝜑𝜃)
ee212.3 (𝜑 → (𝜓𝜏))
ee212.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee212 (𝜑 → (𝜓𝜂))

Proof of Theorem ee212
StepHypRef Expression
1 ee212.1 . 2 (𝜑 → (𝜓𝜒))
2 ee212.2 . . 3 (𝜑𝜃)
32a1d 25 . 2 (𝜑 → (𝜓𝜃))
4 ee212.3 . 2 (𝜑 → (𝜓𝜏))
5 ee212.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
61, 3, 4, 5ee222 41132 1 (𝜑 → (𝜓𝜂))
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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