ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3simpb GIF version

Theorem 3simpb 980
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3simpb ((𝜑𝜓𝜒) → (𝜑𝜒))

Proof of Theorem 3simpb
StepHypRef Expression
1 3ancomb 971 . 2 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
2 3simpa 979 . 2 ((𝜑𝜒𝜓) → (𝜑𝜒))
31, 2sylbi 120 1 ((𝜑𝜓𝜒) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  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:  3adant2  1001  3adantl2  1139  3adantr2  1142  enq0tr  7265  ixxssixx  9714  rebtwn2zlemshrink  10061  zsumdc  11184  muldvds1  11552  dvds2add  11561  dvds2sub  11562  dvdstr  11564  pw2dvdslemn  11877  ctinf  11977
  Copyright terms: Public domain W3C validator