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| Mirrors > Home > MPE Home > Th. List > nffv | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 14-Nov-1995.) (Revised by Mario Carneiro, 15-Oct-2016.) |
| Ref | Expression |
|---|---|
| nffv.1 | ⊢ Ⅎ𝑥𝐹 |
| nffv.2 | ⊢ Ⅎ𝑥𝐴 |
| Ref | Expression |
|---|---|
| nffv | ⊢ Ⅎ𝑥(𝐹‘𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-fv 6569 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑦𝐴𝐹𝑦) | |
| 2 | nffv.2 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 3 | nffv.1 | . . . 4 ⊢ Ⅎ𝑥𝐹 | |
| 4 | nfcv 2905 | . . . 4 ⊢ Ⅎ𝑥𝑦 | |
| 5 | 2, 3, 4 | nfbr 5190 | . . 3 ⊢ Ⅎ𝑥 𝐴𝐹𝑦 |
| 6 | 5 | nfiotaw 6518 | . 2 ⊢ Ⅎ𝑥(℩𝑦𝐴𝐹𝑦) |
| 7 | 1, 6 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥(𝐹‘𝐴) |
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