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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 2169 | . 2 ⊢ Ⅎ𝑥 𝑧 ∈ {𝑦 ∣ 𝜑} |
3 | 2 | nfci 2309 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1460 {cab 2163 Ⅎwnfc 2306 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-nfc 2308 |
This theorem is referenced by: nfaba1 2325 nfrabxy 2658 sbcel12g 3074 sbceqg 3075 nfun 3293 nfpw 3590 nfpr 3644 nfop 3796 nfuni 3817 nfint 3856 intab 3875 nfiunxy 3914 nfiinxy 3915 nfiunya 3916 nfiinya 3917 nfiu1 3918 nfii1 3919 nfopab 4073 nfopab1 4074 nfopab2 4075 repizf2 4164 nfdm 4873 fun11iun 5484 eusvobj2 5864 nfoprab1 5927 nfoprab2 5928 nfoprab3 5929 nfoprab 5930 nfrecs 6311 nffrec 6400 nfixpxy 6720 nfixp1 6721 |
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