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Theorem simp3d 929
 Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)
Hypothesis
Ref Expression
3simp1d.1 (𝜑 → (𝜓𝜒𝜃))
Assertion
Ref Expression
simp3d (𝜑𝜃)

Proof of Theorem simp3d
StepHypRef Expression
1 3simp1d.1 . 2 (𝜑 → (𝜓𝜒𝜃))
2 simp3 917 . 2 ((𝜓𝜒𝜃) → 𝜃)
31, 2syl 14 1 (𝜑𝜃)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ 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:  simp3bi  932  erinxp  6210  addcanprleml  6769  addcanprlemu  6770  ltmprr  6797  lelttrdi  7494  ixxdisj  8872  ixxss1  8873  ixxss2  8874  ixxss12  8875  iccsupr  8935  icodisj  8960  ioom  9216  intfracq  9269  flqdiv  9270  mulqaddmodid  9313  modsumfzodifsn  9345  cjmul  9712
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