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Theorem simpr3 949
Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)
Assertion
Ref Expression
simpr3 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)

Proof of Theorem simpr3
StepHypRef Expression
1 simp3 943 . 2 ((𝜓𝜒𝜃) → 𝜃)
21adantl 271 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)
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:  simplr3  985  simprr3  991  simp1r3  1039  simp2r3  1045  simp3r3  1051  3anandis  1281  isopolem  5562  tfrlemibacc  6045  tfrlemibxssdm  6046  tfrlemibfn  6047  tfr1onlembacc  6061  tfr1onlembxssdm  6062  tfr1onlembfn  6063  tfrcllembacc  6074  tfrcllembxssdm  6075  tfrcllembfn  6076  prloc  6994  prmuloc2  7070  eluzuzle  8959  elioc2  9286  elico2  9287  elicc2  9288  fseq1p1m1  9438  iseqf1olemp  9835  iseqf1oleml  9836  ibcval5  10067  hashdifpr  10124  dvds2ln  10704  divalglemeunn  10796  divalglemex  10797  divalglemeuneg  10798
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