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Mirrors > Home > ILE Home > Th. List > nfpw | GIF version |
Description: Bound-variable hypothesis builder for power class. (Contributed by NM, 28-Oct-2003.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
nfpw.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfpw | ⊢ Ⅎ𝑥𝒫 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pw 3507 | . 2 ⊢ 𝒫 𝐴 = {𝑦 ∣ 𝑦 ⊆ 𝐴} | |
2 | nfcv 2279 | . . . 4 ⊢ Ⅎ𝑥𝑦 | |
3 | nfpw.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | 2, 3 | nfss 3085 | . . 3 ⊢ Ⅎ𝑥 𝑦 ⊆ 𝐴 |
5 | 4 | nfab 2284 | . 2 ⊢ Ⅎ𝑥{𝑦 ∣ 𝑦 ⊆ 𝐴} |
6 | 1, 5 | nfcxfr 2276 | 1 ⊢ Ⅎ𝑥𝒫 𝐴 |
Colors of variables: wff set class |
Syntax hints: {cab 2123 Ⅎwnfc 2266 ⊆ wss 3066 𝒫 cpw 3505 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-in 3072 df-ss 3079 df-pw 3507 |
This theorem is referenced by: (None) |
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