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Theorem simp1r1 1361
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 1241 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant1 1156 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1100
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 198  df-an 385  df-3an 1102
This theorem is referenced by:  trisegint  32477  lshpkrlem6  34913  atbtwnexOLDN  35245  atbtwnex  35246  3dim3  35267  3atlem5  35285  4atlem11  35407  4atexlem7  35873  cdleme22b  36139
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