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Theorem 3bitr2rd 216
 Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr2d.1 (𝜑 → (𝜓𝜒))
3bitr2d.2 (𝜑 → (𝜃𝜒))
3bitr2d.3 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
3bitr2rd (𝜑 → (𝜏𝜓))

Proof of Theorem 3bitr2rd
StepHypRef Expression
1 3bitr2d.1 . . 3 (𝜑 → (𝜓𝜒))
2 3bitr2d.2 . . 3 (𝜑 → (𝜃𝜒))
31, 2bitr4d 190 . 2 (𝜑 → (𝜓𝜃))
4 3bitr2d.3 . 2 (𝜑 → (𝜃𝜏))
53, 4bitr2d 188 1 (𝜑 → (𝜏𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104 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 This theorem is referenced by:  fndmdif  5532  addsubeq4  8000  muleqadd  8452  nn0lt10b  9154  adddivflid  10095  frec2uzltd  10206  mul0inf  11043  summodnegmod  11558  iooref1o  13424
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