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Theorem eel3132 38443
Description: syl2an 494 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
eel3132.1 ((𝜑𝜓) → 𝜒)
eel3132.2 ((𝜃𝜓) → 𝜏)
eel3132.3 ((𝜒𝜏) → 𝜂)
Assertion
Ref Expression
eel3132 ((𝜑𝜃𝜓) → 𝜂)

Proof of Theorem eel3132
StepHypRef Expression
1 eel3132.1 . . 3 ((𝜑𝜓) → 𝜒)
2 eel3132.2 . . 3 ((𝜃𝜓) → 𝜏)
3 eel3132.3 . . 3 ((𝜒𝜏) → 𝜂)
41, 2, 3syl2an 494 . 2 (((𝜑𝜓) ∧ (𝜃𝜓)) → 𝜂)
543impdir 1379 1 ((𝜑𝜃𝜓) → 𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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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