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Theorem simplr3 1010
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 974 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
21adantr 274 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
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 949
This theorem is referenced by:  prarloclemlt  7269  prarloclemlo  7270  resqrexlemdecn  10752  summodclem2  11119  isumss2  11130  ennnfoneleminc  11851  restopnb  12277  blsscls2  12589
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