![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 2600 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2741 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: {cab 2596 Ⅎwnfc 2738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-nfc 2740 |
This theorem is referenced by: nfabd2 2770 abid2f 2777 nfrab1 3099 elabgt 3316 elabgf 3317 nfsbc1d 3420 ss2ab 3633 ab0 3905 abn0 3908 euabsn 4205 iunab 4502 iinab 4517 zfrep4 4707 sniota 5795 opabiotafun 6169 nfixp1 7814 scottexs 8633 scott0s 8634 cp 8637 ofpreima 28848 qqhval2 29354 esum2dlem 29481 sigaclcu2 29510 bnj1366 30154 bnj1321 30349 bnj1384 30354 mptsnunlem 32361 topdifinffinlem 32371 compab 37666 ssfiunibd 38464 setrec2lem2 42240 |
Copyright terms: Public domain | W3C validator |