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Theorem ee211 41284
Description: e211 41283 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee211.1 (𝜑 → (𝜓𝜒))
ee211.2 (𝜑𝜃)
ee211.3 (𝜑𝜏)
ee211.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee211 (𝜑 → (𝜓𝜂))

Proof of Theorem ee211
StepHypRef Expression
1 ee211.1 . 2 (𝜑 → (𝜓𝜒))
2 ee211.2 . . 3 (𝜑𝜃)
32a1d 25 . 2 (𝜑 → (𝜓𝜃))
4 ee211.3 . . 3 (𝜑𝜏)
54a1d 25 . 2 (𝜑 → (𝜓𝜏))
6 ee211.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
71, 3, 5, 6ee222 41128 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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