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Theorem simp1r1 1268
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1r1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜑)

Proof of Theorem simp1r1
StepHypRef Expression
1 simpr1 1193 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant1 1132 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 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:  trisegint  34330  lshpkrlem6  37129  atbtwnexOLDN  37461  atbtwnex  37462  3dim3  37483  3atlem5  37501  4atlem11  37623  4atexlem7  38089  cdleme22b  38355
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