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Theorem simplr3 1008
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simplr3 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)

Proof of Theorem simplr3
StepHypRef Expression
1 simpr3 972 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
21adantr 272 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  prarloclemlt  7265  prarloclemlo  7266  resqrexlemdecn  10724  summodclem2  11091  isumss2  11102  ennnfoneleminc  11819  restopnb  12245  blsscls2  12557
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