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Theorem ee20an 39458
Description: e20an 39457 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee20an.1 (𝜑 → (𝜓𝜒))
ee20an.2 𝜃
ee20an.3 ((𝜒𝜃) → 𝜏)
Assertion
Ref Expression
ee20an (𝜑 → (𝜓𝜏))

Proof of Theorem ee20an
StepHypRef Expression
1 ee20an.1 . 2 (𝜑 → (𝜓𝜒))
2 ee20an.2 . 2 𝜃
3 ee20an.3 . . 3 ((𝜒𝜃) → 𝜏)
43ex 449 . 2 (𝜒 → (𝜃𝜏))
51, 2, 4syl6mpi 67 1 (𝜑 → (𝜓𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 385
This theorem is referenced by: (None)
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