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Theorem ee123 38469
Description: e123 38468 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee123.1 (𝜑𝜓)
ee123.2 (𝜑 → (𝜒𝜃))
ee123.3 (𝜑 → (𝜒 → (𝜏𝜂)))
ee123.4 (𝜓 → (𝜃 → (𝜂𝜁)))
Assertion
Ref Expression
ee123 (𝜑 → (𝜒 → (𝜏𝜁)))

Proof of Theorem ee123
StepHypRef Expression
1 ee123.1 . . . 4 (𝜑𝜓)
21a1d 25 . . 3 (𝜑 → (𝜏𝜓))
32a1d 25 . 2 (𝜑 → (𝜒 → (𝜏𝜓)))
4 ee123.2 . . 3 (𝜑 → (𝜒𝜃))
54a1dd 50 . 2 (𝜑 → (𝜒 → (𝜏𝜃)))
6 ee123.3 . 2 (𝜑 → (𝜒 → (𝜏𝜂)))
7 ee123.4 . 2 (𝜓 → (𝜃 → (𝜂𝜁)))
83, 5, 6, 7ee333 38192 1 (𝜑 → (𝜒 → (𝜏𝜁)))
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: (None)
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