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Theorem simp1r3 1157
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 1067 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant1 1080 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 197  df-an 386  df-3an 1038
This theorem is referenced by:  lshpkrlem6  33917  atbtwnexOLDN  34248  atbtwnex  34249  3dim3  34270  3atlem5  34288  lplnle  34341  4atlem11  34410  4atexlem7  34876  cdleme22b  35144  stoweidlem60  39610
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