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Theorem ee23an 38452
Description: e23an 38451 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee23an.1 (𝜑 → (𝜓𝜒))
ee23an.2 (𝜑 → (𝜓 → (𝜃𝜏)))
ee23an.3 ((𝜒𝜏) → 𝜂)
Assertion
Ref Expression
ee23an (𝜑 → (𝜓 → (𝜃𝜂)))

Proof of Theorem ee23an
StepHypRef Expression
1 ee23an.1 . . 3 (𝜑 → (𝜓𝜒))
21a1dd 50 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
3 ee23an.2 . 2 (𝜑 → (𝜓 → (𝜃𝜏)))
4 ee23an.3 . 2 ((𝜒𝜏) → 𝜂)
52, 3, 4ee33an 38431 1 (𝜑 → (𝜓 → (𝜃𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator