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Theorem ee323 38182
Description: e323 38461 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee323.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee323.2 (𝜑 → (𝜓𝜏))
ee323.3 (𝜑 → (𝜓 → (𝜒𝜂)))
ee323.4 (𝜃 → (𝜏 → (𝜂𝜁)))
Assertion
Ref Expression
ee323 (𝜑 → (𝜓 → (𝜒𝜁)))

Proof of Theorem ee323
StepHypRef Expression
1 ee323.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee323.2 . . 3 (𝜑 → (𝜓𝜏))
32a1dd 50 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
4 ee323.3 . 2 (𝜑 → (𝜓 → (𝜒𝜂)))
5 ee323.4 . 2 (𝜃 → (𝜏 → (𝜂𝜁)))
61, 3, 4, 5ee333 38181 1 (𝜑 → (𝜓 → (𝜒𝜁)))
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 386  df-3an 1038
This theorem is referenced by:  e323  38461  trintALT  38586
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