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Theorem simpr1 947
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 941 . 2 ((𝜓𝜒𝜃) → 𝜓)
21adantl 271 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by:  simplr1  983  simprr1  989  simp1r1  1037  simp2r1  1043  simp3r1  1049  3anandis  1281  isopolem  5562  caovlem2d  5794  tfrlemibacc  6045  tfrlemibfn  6047  tfr1onlembacc  6061  tfr1onlembfn  6063  tfrcllembacc  6074  tfrcllembfn  6076  eqsupti  6635  prmuloc2  7070  elioc2  9286  elico2  9287  elicc2  9288  fseq1p1m1  9438  elfz0ubfz0  9464  ico0  9601  iseqf1olemp  9836  iseqf1oleml  9837  ibcval5  10068  isumss2  10673  dvds2ln  10711  divalglemeunn  10803  divalglemex  10804  divalglemeuneg  10805  qredeq  10960  findset  11285
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