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Theorem ee012 41294
Description: e012 41293 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee012.1 𝜑
ee012.2 (𝜓𝜒)
ee012.3 (𝜓 → (𝜃𝜏))
ee012.4 (𝜑 → (𝜒 → (𝜏𝜂)))
Assertion
Ref Expression
ee012 (𝜓 → (𝜃𝜂))

Proof of Theorem ee012
StepHypRef Expression
1 ee012.1 . . . 4 𝜑
21a1i 11 . . 3 (𝜃𝜑)
32a1i 11 . 2 (𝜓 → (𝜃𝜑))
4 ee012.2 . . 3 (𝜓𝜒)
54a1d 25 . 2 (𝜓 → (𝜃𝜒))
6 ee012.3 . 2 (𝜓 → (𝜃𝜏))
7 ee012.4 . 2 (𝜑 → (𝜒 → (𝜏𝜂)))
83, 5, 6, 7ee222 41128 1 (𝜓 → (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