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Theorem simpr1 921
 Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)
Assertion
Ref Expression
simpr1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)

Proof of Theorem simpr1
StepHypRef Expression
1 simp1 915 . 2 ((𝜓𝜒𝜃) → 𝜓)
21adantl 266 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 101   ∧ w3a 896 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105 This theorem depends on definitions:  df-bi 114  df-3an 898 This theorem is referenced by:  simplr1  957  simprr1  963  simp1r1  1011  simp2r1  1017  simp3r1  1023  3anandis  1253  isopolem  5489  caovlem2d  5721  tfrlemibacc  5971  tfrlemibfn  5973  eqsupti  6402  prmuloc2  6723  elioc2  8906  elico2  8907  elicc2  8908  fseq1p1m1  9058  elfz0ubfz0  9084  ico0  9218  ibcval5  9631  dvds2ln  10140  divalglemeunn  10233  divalglemex  10234  divalglemeuneg  10235  findset  10457
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