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Theorem simp2l1 1267
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp2l1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Proof of Theorem simp2l1
StepHypRef Expression
1 simpl1 1186 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant2 1129 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1082
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 209  df-an 399  df-3an 1084
This theorem is referenced by:  btwnconn1lem8  33548  btwnconn1lem11  33551  btwnconn1lem12  33552  2lplnja  36747  cdlemk21-2N  38019  cdlemk19xlem  38070  jm2.27  39595
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