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Theorem simp1r1 1263
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 1188 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant1 1127 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1081
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 208  df-an 397  df-3an 1083
This theorem is referenced by:  trisegint  33392  lshpkrlem6  36137  atbtwnexOLDN  36469  atbtwnex  36470  3dim3  36491  3atlem5  36509  4atlem11  36631  4atexlem7  37097  cdleme22b  37363
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