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Theorem simp3l2 1382
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l2 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simp3l2
StepHypRef Expression
1 simpl2 1248 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant3 1169 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  w3a 1111
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 199  df-an 387  df-3an 1113
This theorem is referenced by:  cvmlift2lem10  31836  cdleme36m  36531  cdlemk5u  36931  cdlemk6u  36932  cdlemk21N  36943  cdlemk20  36944  cdlemk27-3  36977  cdlemk28-3  36978
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