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Mirrors > Home > MPE Home > Th. List > nfab1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfab1 | ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfsab1 2810 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2966 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: {cab 2801 Ⅎwnfc 2963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-nfc 2965 |
This theorem is referenced by: nfabd2 3004 nfabd2OLD 3005 abid2f 3014 abeq2f 3015 nfrab1 3386 elabgt 3665 elabgf 3666 elabg 3668 nfsbc1d 3792 ss2ab 4041 ab0 4335 abn0 4338 euabsn 4664 iunab 4977 iinab 4992 zfrep4 5202 rnep 5799 sniota 6348 opabiotafun 6746 nfixp1 8484 scottexs 9318 scott0s 9319 cp 9322 symgval 18499 ofpreima 30412 qqhval2 31225 esum2dlem 31353 sigaclcu2 31381 bnj1366 32103 bnj1321 32301 bnj1384 32306 currysetlem 34258 currysetlem1 34260 bj-reabeq 34341 mptsnunlem 34621 topdifinffinlem 34630 scottabf 40583 compab 40781 ssfiunibd 41583 absnsb 43269 setrec2lem2 44804 |
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