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Mirrors > Home > MPE Home > Th. List > bibi1 | Structured version Visualization version GIF version |
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 335 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 |
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 199 |
This theorem is referenced by: bitr3 344 bitr 841 eqeq1d 2827 sbeqalb 3715 isclo2 21263 sbc3orgVD 39905 trsbcVD 39931 sbcssgVD 39937 csbingVD 39938 csbsngVD 39947 csbxpgVD 39948 csbrngVD 39950 csbunigVD 39952 csbfv12gALTVD 39953 e2ebindVD 39966 |
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