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| Mirrors > Home > MPE Home > Th. List > bitrid | Structured version Visualization version GIF version | ||
| Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993.) |
| Ref | Expression |
|---|---|
| bitrid.1 | ⊢ (𝜑 ↔ 𝜓) |
| bitrid.2 | ⊢ (𝜒 → (𝜓 ↔ 𝜃)) |
| Ref | Expression |
|---|---|
| bitrid | ⊢ (𝜒 → (𝜑 ↔ 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bitrid.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜒 → (𝜑 ↔ 𝜓)) |
| 3 | bitrid.2 | . 2 ⊢ (𝜒 → (𝜓 ↔ 𝜃)) | |
| 4 | 2, 3 | bitrd 279 | 1 ⊢ (𝜒 → (𝜑 ↔ 𝜃)) |
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