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Mirrors > Home > MPE Home > Th. List > nfpw | Structured version Visualization version 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 4560 | . 2 ⊢ 𝒫 𝐴 = {𝑦 ∣ 𝑦 ⊆ 𝐴} | |
2 | nfcv 2905 | . . . 4 ⊢ Ⅎ𝑥𝑦 | |
3 | nfpw.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | 2, 3 | nfss 3934 | . . 3 ⊢ Ⅎ𝑥 𝑦 ⊆ 𝐴 |
5 | 4 | nfab 2911 | . 2 ⊢ Ⅎ𝑥{𝑦 ∣ 𝑦 ⊆ 𝐴} |
6 | 1, 5 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥𝒫 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: {cab 2713 Ⅎwnfc 2885 ⊆ wss 3908 𝒫 cpw 4558 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-nf 1786 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2887 df-ral 3063 df-v 3445 df-in 3915 df-ss 3925 df-pw 4560 |
This theorem is referenced by: esum2d 32520 ldsysgenld 32587 stoweidlem57 44193 sge0iunmptlemre 44551 nfafv2 45345 |
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