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Theorem ee10an 39238
Description: e10an 39237 without virtual deductions. sylancl 695 is also e10an 39237 without virtual deductions, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee10an.1 (𝜑𝜓)
ee10an.2 𝜒
ee10an.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ee10an (𝜑𝜃)

Proof of Theorem ee10an
StepHypRef Expression
1 ee10an.1 . 2 (𝜑𝜓)
2 ee10an.2 . 2 𝜒
3 ee10an.3 . 2 ((𝜓𝜒) → 𝜃)
41, 2, 3sylancl 695 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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