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Theorem eel2131 40925
Description: syl2an 595 with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016.)
Hypotheses
Ref Expression
eel2131.1 ((𝜑𝜓) → 𝜒)
eel2131.2 ((𝜑𝜃) → 𝜏)
eel2131.3 ((𝜒𝜏) → 𝜂)
Assertion
Ref Expression
eel2131 ((𝜑𝜓𝜃) → 𝜂)

Proof of Theorem eel2131
StepHypRef Expression
1 eel2131.1 . . 3 ((𝜑𝜓) → 𝜒)
2 eel2131.2 . . 3 ((𝜑𝜃) → 𝜏)
3 eel2131.3 . . 3 ((𝜒𝜏) → 𝜂)
41, 2, 3syl2an 595 . 2 (((𝜑𝜓) ∧ (𝜑𝜃)) → 𝜂)
543impdi 1342 1 ((𝜑𝜓𝜃) → 𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by: (None)
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