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Theorem simpr1l 1003
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr1l ((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)

Proof of Theorem simpr1l
StepHypRef Expression
1 simp1l 970 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)
21adantl 272 1 ((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 929
This theorem is referenced by:  prcdnql  7140  prnmaxl  7144
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