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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 2175 | . 2 ⊢ ℲxA | |
2 | 1 | nfsbc1 2775 | 1 ⊢ Ⅎx[A / x]φ |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1346 [wsbc 2758 |
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-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-sbc 2759 |
This theorem is referenced by: elrabsf 2795 cbvralcsf 2902 cbvrexcsf 2903 euotd 3982 findes 4269 ralrnmpt 5252 rexrnmpt 5253 dfopab2 5757 dfoprab3s 5758 mpt2xopoveq 5796 indpi 6326 nn0ind-raph 8131 uzind4s 8309 indstr 8312 fzrevral 8737 bj-bdfindes 9409 bj-findes 9441 |
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