![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > nfab | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfab.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfab | ⊢ Ⅎ𝑥{𝑦 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfab.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nfsab 2602 | . 2 ⊢ Ⅎ𝑥 𝑧 ∈ {𝑦 ∣ 𝜑} |
3 | 2 | nfci 2741 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1699 {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-11 2021 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: nfaba1 2756 nfun 3731 sbcel12 3935 sbceqg 3936 nfpw 4120 nfpr 4179 nfuni 4378 nfint 4421 intab 4442 nfiun 4484 nfiin 4485 nfiu1 4486 nfii1 4487 nfopab 4650 nfopab1 4651 nfopab2 4652 nfdm 5288 eusvobj2 6542 nfoprab1 6602 nfoprab2 6603 nfoprab3 6604 nfoprab 6605 fun11iun 7019 nfwrecs 7296 nfixp 7813 nfixp1 7814 reclem2pr 9749 nfwrd 13188 mreiincl 16079 lss1d 18784 disjabrex 28777 disjabrexf 28778 esumc 29440 bnj900 30253 bnj1014 30284 bnj1123 30308 bnj1307 30345 bnj1398 30356 bnj1444 30365 bnj1445 30366 bnj1446 30367 bnj1447 30368 bnj1467 30376 bnj1518 30386 bnj1519 30387 dfon2lem3 30934 bj-xnex 32245 sdclem1 32709 heibor1 32779 dihglblem5 35605 sbcel12gOLD 37775 ssfiunibd 38464 hoidmvlelem1 39485 nfsetrecs 42232 setrec2lem2 42240 setrec2 42241 |
Copyright terms: Public domain | W3C validator |