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| Mirrors > Home > MPE Home > Th. List > nfcxfr | Structured version Visualization version GIF version | ||
| Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.) |
| Ref | Expression |
|---|---|
| nfcxfr.1 | ⊢ 𝐴 = 𝐵 |
| nfcxfr.2 | ⊢ Ⅎ𝑥𝐵 |
| Ref | Expression |
|---|---|
| nfcxfr | ⊢ Ⅎ𝑥𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfcxfr.2 | . 2 ⊢ Ⅎ𝑥𝐵 | |
| 2 | nfcxfr.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
| 3 | 2 | nfceqi 2902 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵) |
| 4 | 1, 3 | mpbir 231 | 1 ⊢ Ⅎ𝑥𝐴 |
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