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Mirrors > Home > ILE Home > Th. List > nfsbc | Unicode version |
Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 7-Sep-2014.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfsbc.1 | |
nfsbc.2 |
Ref | Expression |
---|---|
nfsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1427 | . . 3 | |
2 | nfsbc.1 | . . . 4 | |
3 | 2 | a1i 9 | . . 3 |
4 | nfsbc.2 | . . . 4 | |
5 | 4 | a1i 9 | . . 3 |
6 | 1, 3, 5 | nfsbcd 2901 | . 2 |
7 | 6 | mptru 1325 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1317 wnf 1421 wnfc 2245 wsbc 2882 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-sbc 2883 |
This theorem is referenced by: cbvralcsf 3032 cbvrexcsf 3033 opelopabf 4166 ralrnmpt 5530 rexrnmpt 5531 dfopab2 6055 dfoprab3s 6056 mpoxopoveq 6105 |
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