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Theorem simp2l1 1271
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 1190 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant2 1133 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)
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:  btwnconn1lem8  34392  btwnconn1lem11  34395  btwnconn1lem12  34396  2lplnja  37629  cdlemk21-2N  38901  cdlemk19xlem  38952  jm2.27  40827
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