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| Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.) | 
| Ref | Expression | 
|---|---|
| pm5.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ↔ 𝜓)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | pm5.501 366 | . 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 ↔ 𝜓))) | |
| 2 | 1 | biimpa 476 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ↔ 𝜓)) | 
| 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: pm5.35 825 impimprbi 828 ssconb 4141 raaan 4516 raaanv 4517 raaan2 4520 suppimacnvss 8199 mdsymi 32431 ply1degltel 33616 ply1degleel 33617 tsbi1 38141 abnotbtaxb 46932 elprneb 47046 | 
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