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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 4499 | . 2 ⊢ 𝒫 𝐴 = {𝑦 ∣ 𝑦 ⊆ 𝐴} | |
2 | nfcv 2955 | . . . 4 ⊢ Ⅎ𝑥𝑦 | |
3 | nfpw.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | 2, 3 | nfss 3907 | . . 3 ⊢ Ⅎ𝑥 𝑦 ⊆ 𝐴 |
5 | 4 | nfab 2961 | . 2 ⊢ Ⅎ𝑥{𝑦 ∣ 𝑦 ⊆ 𝐴} |
6 | 1, 5 | nfcxfr 2953 | 1 ⊢ Ⅎ𝑥𝒫 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: {cab 2776 Ⅎwnfc 2936 ⊆ wss 3881 𝒫 cpw 4497 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ral 3111 df-v 3443 df-in 3888 df-ss 3898 df-pw 4499 |
This theorem is referenced by: esum2d 31462 ldsysgenld 31529 stoweidlem57 42699 sge0iunmptlemre 43054 nfafv2 43774 |
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