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Theorem ee11an 39232
Description: e11an 39231 without virtual deductions. syl22anc 1367 is also e11an 39231 without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee11an.1 (𝜑𝜓)
ee11an.2 (𝜑𝜒)
ee11an.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ee11an (𝜑𝜃)

Proof of Theorem ee11an
StepHypRef Expression
1 ee11an.1 . 2 (𝜑𝜓)
2 ee11an.2 . 2 (𝜑𝜒)
3 ee11an.3 . . 3 ((𝜓𝜒) → 𝜃)
43ex 449 . 2 (𝜓 → (𝜒𝜃))
51, 2, 4sylc 65 1 (𝜑𝜃)
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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