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| Mirrors > Home > MPE Home > Th. List > nfov | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for operation value. (Contributed by NM, 4-May-2004.) |
| Ref | Expression |
|---|---|
| nfov.1 | ⊢ Ⅎ𝑥𝐴 |
| nfov.2 | ⊢ Ⅎ𝑥𝐹 |
| nfov.3 | ⊢ Ⅎ𝑥𝐵 |
| Ref | Expression |
|---|---|
| nfov | ⊢ Ⅎ𝑥(𝐴𝐹𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfov.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
| 3 | nfov.2 | . . . 4 ⊢ Ⅎ𝑥𝐹 | |
| 4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐹) |
| 5 | nfov.3 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
| 6 | 5 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
| 7 | 2, 4, 6 | nfovd 7460 | . 2 ⊢ (⊤ → Ⅎ𝑥(𝐴𝐹𝐵)) |
| 8 | 7 | mptru 1547 | 1 ⊢ Ⅎ𝑥(𝐴𝐹𝐵) |
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