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Mirrors > Home > MPE Home > Th. List > bitr4id | Structured version Visualization version GIF version |
Description: A syllogism inference from two biconditionals. (Contributed by NM, 25-Nov-1994.) |
Ref | Expression |
---|---|
bitr4id.2 | ⊢ (𝜓 ↔ 𝜒) |
bitr4id.1 | ⊢ (𝜑 → (𝜃 ↔ 𝜒)) |
Ref | Expression |
---|---|
bitr4id | ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr4id.1 | . 2 ⊢ (𝜑 → (𝜃 ↔ 𝜒)) | |
2 | bitr4id.2 | . . 3 ⊢ (𝜓 ↔ 𝜒) | |
3 | 2 | bicomi 227 | . 2 ⊢ (𝜒 ↔ 𝜓) |
4 | 1, 3 | bitr2di 292 | 1 ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
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