Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  3imtr3g GIF version

Theorem 3imtr3g 193
 Description: More general version of 3imtr3i 189. Useful for converting definitions in a formula. (Contributed by NM, 20-May-1996.) (Proof shortened by Wolf Lammen, 20-Dec-2013.)
Hypotheses
Ref Expression
3imtr3g.1 (𝜑 → (𝜓𝜒))
3imtr3g.2 (𝜓𝜃)
3imtr3g.3 (𝜒𝜏)
Assertion
Ref Expression
3imtr3g (𝜑 → (𝜃𝜏))

Proof of Theorem 3imtr3g
StepHypRef Expression
1 3imtr3g.2 . . 3 (𝜓𝜃)
2 3imtr3g.1 . . 3 (𝜑 → (𝜓𝜒))
31, 2syl5bir 142 . 2 (𝜑 → (𝜃𝜒))
4 3imtr3g.3 . 2 (𝜒𝜏)
53, 4syl6ib 150 1 (𝜑 → (𝜃𝜏))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  dvelimfALT2  1698  dvelimf  1891  dveeq1  1895  sspwb  3952  ssopab2b  4013  wetrep  4097  imadif  4979  ssoprab2b  5562  iinerm  6178  uzind  8349
 Copyright terms: Public domain W3C validator