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Theorem simp3l2 1278
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 1191 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1086
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 206  df-an 397  df-3an 1088
This theorem is referenced by:  cvmlift2lem10  33282  poxp3  33804  cdleme36m  38483  cdlemk5u  38883  cdlemk6u  38884  cdlemk21N  38895  cdlemk20  38896  cdlemk27-3  38929  cdlemk28-3  38930
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