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Theorem simp2l3 1271
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp2l3 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Proof of Theorem simp2l3
StepHypRef Expression
1 simpl3 1190 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
213ad2ant2 1131 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  btwnconn1lem8  33563  btwnconn1lem12  33567  2lplnja  36801  cdlemk21-2N  38073  cdlemk19xlem  38124  jm2.27  39760
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