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Theorem ee112 41281
Description: e112 41280 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee112.1 (𝜑𝜓)
ee112.2 (𝜑𝜒)
ee112.3 (𝜑 → (𝜃𝜏))
ee112.4 (𝜓 → (𝜒 → (𝜏𝜂)))
Assertion
Ref Expression
ee112 (𝜑 → (𝜃𝜂))

Proof of Theorem ee112
StepHypRef Expression
1 ee112.1 . . 3 (𝜑𝜓)
21a1d 25 . 2 (𝜑 → (𝜃𝜓))
3 ee112.2 . . 3 (𝜑𝜒)
43a1d 25 . 2 (𝜑 → (𝜃𝜒))
5 ee112.3 . 2 (𝜑 → (𝜃𝜏))
6 ee112.4 . 2 (𝜓 → (𝜒 → (𝜏𝜂)))
72, 4, 5, 6ee222 41128 1 (𝜑 → (𝜃𝜂))
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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