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Theorem ee002 41270
Description: e002 41269 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee002.1 𝜑
ee002.2 𝜓
ee002.3 (𝜒 → (𝜃𝜏))
ee002.4 (𝜑 → (𝜓 → (𝜏𝜂)))
Assertion
Ref Expression
ee002 (𝜒 → (𝜃𝜂))

Proof of Theorem ee002
StepHypRef Expression
1 ee002.1 . . . 4 𝜑
21a1i 11 . . 3 (𝜃𝜑)
32a1i 11 . 2 (𝜒 → (𝜃𝜑))
4 ee002.2 . . . 4 𝜓
54a1i 11 . . 3 (𝜃𝜓)
65a1i 11 . 2 (𝜒 → (𝜃𝜓))
7 ee002.3 . 2 (𝜒 → (𝜃𝜏))
8 ee002.4 . 2 (𝜑 → (𝜓 → (𝜏𝜂)))
93, 6, 7, 8ee222 41128 1 (𝜒 → (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)
  Copyright terms: Public domain W3C validator