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Mirrors > Home > MPE Home > Th. List > bitrdi | Structured version Visualization version GIF version |
Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
bitrdi.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
bitrdi.2 | ⊢ (𝜒 ↔ 𝜃) |
Ref | Expression |
---|---|
bitrdi | ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitrdi.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | bitrdi.2 | . . 3 ⊢ (𝜒 ↔ 𝜃) | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → (𝜒 ↔ 𝜃)) |
4 | 1, 3 | bitrd 282 | 1 ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
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