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Mirrors > Home > ILE Home > Th. List > nfsbc1v | GIF version |
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfsbc1v | ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2220 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | nfsbc1 2833 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1390 [wsbc 2816 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-sbc 2817 |
This theorem is referenced by: elrabsf 2853 cbvralcsf 2965 cbvrexcsf 2966 euotd 4017 findes 4352 ralrnmpt 5341 rexrnmpt 5342 dfopab2 5846 dfoprab3s 5847 mpt2xopoveq 5889 findcard2 6423 findcard2s 6424 ac6sfi 6431 indpi 6594 nn0ind-raph 8545 uzind4s 8759 indstr 8762 fzrevral 9198 exfzdc 9326 uzsinds 9518 zsupcllemstep 10485 infssuzex 10489 prmind2 10646 bj-bdfindes 10902 bj-findes 10934 |
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