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Theorem simp1r3 1263
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1r3 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜒)

Proof of Theorem simp1r3
StepHypRef Expression
1 simpr3 1188 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant1 1125 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 1081
This theorem is referenced by:  lshpkrlem6  36131  atbtwnexOLDN  36463  atbtwnex  36464  3dim3  36485  3atlem5  36503  lplnle  36556  4atlem11  36625  4atexlem7  37091  cdleme22b  37357  stoweidlem60  42222
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