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Theorem ee021 41292
Description: e021 41291 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee021.1 𝜑
ee021.2 (𝜓 → (𝜒𝜃))
ee021.3 (𝜓𝜏)
ee021.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee021 (𝜓 → (𝜒𝜂))

Proof of Theorem ee021
StepHypRef Expression
1 ee021.1 . . . 4 𝜑
21a1i 11 . . 3 (𝜒𝜑)
32a1i 11 . 2 (𝜓 → (𝜒𝜑))
4 ee021.2 . 2 (𝜓 → (𝜒𝜃))
5 ee021.3 . . 3 (𝜓𝜏)
65a1d 25 . 2 (𝜓 → (𝜒𝜏))
7 ee021.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
83, 4, 6, 7ee222 41128 1 (𝜓 → (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 210  df-an 400
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator