| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > nfbr | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 14-Oct-2016.) |
| Ref | Expression |
|---|---|
| nfbr.1 | ⊢ Ⅎ𝑥𝐴 |
| nfbr.2 | ⊢ Ⅎ𝑥𝑅 |
| nfbr.3 | ⊢ Ⅎ𝑥𝐵 |
| Ref | Expression |
|---|---|
| nfbr | ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfbr.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
| 3 | nfbr.2 | . . . 4 ⊢ Ⅎ𝑥𝑅 | |
| 4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝑅) |
| 5 | nfbr.3 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
| 6 | 5 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
| 7 | 2, 4, 6 | nfbrd 5189 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴𝑅𝐵) |
| 8 | 7 | mptru 1547 | 1 ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
| Copyright terms: Public domain | W3C validator |