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| Description: Theorem *4.86 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) | 
| Ref | Expression | 
|---|---|
| bibi1 | ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
| 2 | 1 | bibi1d 343 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ↔ wb 206 | 
| 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 | 
| This theorem is referenced by: bitr3 352 bitr 805 eqeq1d 2739 sbeqalb 3853 isclo2 23096 sbc3orgVD 44871 trsbcVD 44897 sbcssgVD 44903 csbingVD 44904 csbsngVD 44913 csbxpgVD 44914 csbrngVD 44916 csbunigVD 44918 csbfv12gALTVD 44919 e2ebindVD 44932 | 
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