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Mirrors > Home > MPE Home > Th. List > bitr3 | Structured version Visualization version GIF version |
Description: Closed nested implication form of bitr3i 266. Derived automatically from bitr3VD 39084. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
bitr3 | ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bibi1 341 | . 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒))) | |
2 | 1 | biimpd 219 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 |
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 197 |
This theorem is referenced by: sumodd 15111 3orbi123VD 39085 sbc3orgVD 39086 trsbcVD 39113 csbrngVD 39132 e2ebindVD 39148 e2ebindALT 39165 |
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