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Theorem ee122 39029
Description: e122 39195 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee122.1 (𝜑𝜓)
ee122.2 (𝜑 → (𝜒𝜃))
ee122.3 (𝜑 → (𝜒𝜏))
ee122.4 (𝜓 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee122 (𝜑 → (𝜒𝜂))

Proof of Theorem ee122
StepHypRef Expression
1 ee122.1 . . 3 (𝜑𝜓)
21a1d 25 . 2 (𝜑 → (𝜒𝜓))
3 ee122.2 . 2 (𝜑 → (𝜒𝜃))
4 ee122.3 . 2 (𝜑 → (𝜒𝜏))
5 ee122.4 . 2 (𝜓 → (𝜃 → (𝜏𝜂)))
62, 3, 4, 5ee222 39025 1 (𝜑 → (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 197  df-an 385
This theorem is referenced by:  tratrb  39063
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