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Theorem eel132 39244
Description: syl2an 493 with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016.)
Hypotheses
Ref Expression
eel132.1 (𝜑𝜓)
eel132.2 ((𝜒𝜃) → 𝜏)
eel132.3 ((𝜓𝜏) → 𝜂)
Assertion
Ref Expression
eel132 ((𝜑𝜒𝜃) → 𝜂)

Proof of Theorem eel132
StepHypRef Expression
1 eel132.1 . . 3 (𝜑𝜓)
2 eel132.2 . . 3 ((𝜒𝜃) → 𝜏)
3 eel132.3 . . 3 ((𝜓𝜏) → 𝜂)
41, 2, 3syl2an 493 . 2 ((𝜑 ∧ (𝜒𝜃)) → 𝜂)
543impb 1279 1 ((𝜑𝜒𝜃) → 𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1054
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  df-3an 1056
This theorem is referenced by: (None)
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