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Mirrors > Home > MPE Home > Th. List > bitr3d | Structured version Visualization version GIF version |
Description: Deduction form of bitr3i 280. (Contributed by NM, 14-May-1993.) |
Ref | Expression |
---|---|
bitr3d.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
bitr3d.2 | ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
Ref | Expression |
---|---|
bitr3d | ⊢ (𝜑 → (𝜒 ↔ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr3d.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | bicomd 226 | . 2 ⊢ (𝜑 → (𝜒 ↔ 𝜓)) |
3 | bitr3d.2 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜃)) | |
4 | 2, 3 | bitrd 282 | 1 ⊢ (𝜑 → (𝜒 ↔ 𝜃)) |
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