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Mirrors > Home > MPE Home > Th. List > bitr3 | Structured version Visualization version GIF version |
Description: Closed nested implication form of bitr3i 276. Derived automatically from bitr3VD 42469. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
bitr3 | ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bibi1 352 | . 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) | |
2 | 1 | biimpd 228 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 |
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 206 |
This theorem is referenced by: sumodd 16097 3orbi123VD 42470 sbc3orgVD 42471 trsbcVD 42497 csbrngVD 42516 e2ebindVD 42532 e2ebindALT 42549 |
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