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| Description: Theorem *4.22 of [WhiteheadRussell] p. 117. bitri 275 in closed form. (Contributed by NM, 3-Jan-2005.) | 
| Ref | Expression | 
|---|---|
| bitr | ⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜑 ↔ 𝜒)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bibi1 351 | . 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) | |
| 2 | 1 | biimpar 477 | 1 ⊢ (((𝜑 ↔ 𝜓) ∧ (𝜓 ↔ 𝜒)) → (𝜑 ↔ 𝜒)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ↔ wb 206 ∧ wa 395 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 | 
| This theorem depends on definitions: df-bi 207 df-an 396 | 
| This theorem is referenced by: opelopabt 5537 domunfican 9361 albitr 44382 3orbi123VD 44870 e2ebindALT 44949 | 
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