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Theorem simpr3 947
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 941 . 2 ((𝜓𝜒𝜃) → 𝜃)
21adantl 271 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
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 922
This theorem is referenced by:  simplr3  983  simprr3  989  simp1r3  1037  simp2r3  1043  simp3r3  1049  3anandis  1279  isopolem  5540  tfrlemibacc  6023  tfrlemibxssdm  6024  tfrlemibfn  6025  tfr1onlembacc  6039  tfr1onlembxssdm  6040  tfr1onlembfn  6041  tfrcllembacc  6052  tfrcllembxssdm  6053  tfrcllembfn  6054  prloc  6953  prmuloc2  7029  eluzuzle  8922  elioc2  9249  elico2  9250  elicc2  9251  fseq1p1m1  9401  ibcval5  10006  hashdifpr  10063  dvds2ln  10609  divalglemeunn  10701  divalglemex  10702  divalglemeuneg  10703
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