ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp3d GIF version

Theorem simp3d 996
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 984 . 2 ((𝜓𝜒𝜃) → 𝜃)
31, 2syl 14 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  simp3bi  999  erinxp  6510  resixp  6634  addcanprleml  7445  addcanprlemu  7446  ltmprr  7473  lelttrdi  8211  ixxdisj  9715  ixxss1  9716  ixxss2  9717  ixxss12  9718  iccsupr  9778  icodisj  9804  ioom  10068  intfracq  10123  flqdiv  10124  mulqaddmodid  10167  modsumfzodifsn  10199  cjmul  10688  sumtp  11214  crth  11934  ennnfonelemim  11971  ctiunct  11987  strsetsid  12029  strleund  12084  lmcvg  12423  lmff  12455  lmtopcnp  12456  xmeter  12642  xmetresbl  12646  tgqioo  12753  ivthinclemlopn  12820  ivthinclemuopn  12822  limccl  12834  limcdifap  12837  limcresi  12841  limccnpcntop  12850  limccnp2lem  12851  limccnp2cntop  12852  limccoap  12853  cosordlem  12976  relogbval  13074  relogbzcl  13075  nnlogbexp  13082
  Copyright terms: Public domain W3C validator