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| Mirrors > Home > MPE Home > Th. List > mpbir2an | Structured version Visualization version GIF version | ||
| Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 10-May-2005.) |
| Ref | Expression |
|---|---|
| mpbir2an.1 | ⊢ 𝜓 |
| mpbir2an.2 | ⊢ 𝜒 |
| mpbir2an.maj | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) |
| Ref | Expression |
|---|---|
| mpbir2an | ⊢ 𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpbir2an.2 | . 2 ⊢ 𝜒 | |
| 2 | mpbir2an.1 | . . 3 ⊢ 𝜓 | |
| 3 | mpbir2an.maj | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) | |
| 4 | 2, 3 | mpbiran 709 | . 2 ⊢ (𝜑 ↔ 𝜒) |
| 5 | 1, 4 | mpbir 231 | 1 ⊢ 𝜑 |
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