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Theorem simpr1l 1038
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 1005 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)
21adantl 275 1 ((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
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 964
This theorem is referenced by:  prcdnql  7306  prnmaxl  7310  neitx  12453
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