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Theorem simpr2 922
 Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)
Assertion
Ref Expression
simpr2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)

Proof of Theorem simpr2
StepHypRef Expression
1 simp2 916 . 2 ((𝜓𝜒𝜃) → 𝜒)
21adantl 266 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)
 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:  simplr2  958  simprr2  964  simp1r2  1012  simp2r2  1018  simp3r2  1024  3anandis  1253  isopolem  5488  tfrlemibacc  5970  tfrlemibfn  5972  prltlu  6642  prdisj  6647  prmuloc2  6722  eluzuzle  8576  elioc2  8905  elico2  8906  elicc2  8907  fseq1p1m1  9057  fz0fzelfz0  9085  ibcval5  9630  dvds2ln  10139
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