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Mirrors > Home > ILE Home > Th. List > nfab | 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 2029 | . 2 ⊢ Ⅎx z ∈ {y ∣ φ} |
3 | 2 | nfci 2165 | 1 ⊢ Ⅎx{y ∣ φ} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1346 {cab 2023 Ⅎwnfc 2162 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-nfc 2164 |
This theorem is referenced by: nfaba1 2180 nfrabxy 2484 sbcel12g 2859 sbceqg 2860 nfun 3093 nfpw 3363 nfpr 3411 nfop 3556 nfuni 3577 nfint 3616 intab 3635 nfiunxy 3674 nfiinxy 3675 nfiunya 3676 nfiinya 3677 nfiu1 3678 nfii1 3679 nfopab 3816 nfopab1 3817 nfopab2 3818 repizf2 3906 nfdm 4521 fun11iun 5090 eusvobj2 5441 nfoprab1 5496 nfoprab2 5497 nfoprab3 5498 nfoprab 5499 nfrecs 5863 nffrec 5921 |
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