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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 1442 | . . 3 | |
2 | nfsbc.1 | . . . 4 | |
3 | 2 | a1i 9 | . . 3 |
4 | nfsbc.2 | . . . 4 | |
5 | 4 | a1i 9 | . . 3 |
6 | 1, 3, 5 | nfsbcd 2923 | . 2 |
7 | 6 | mptru 1340 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1332 wnf 1436 wnfc 2266 wsbc 2904 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-sbc 2905 |
This theorem is referenced by: cbvralcsf 3057 cbvrexcsf 3058 opelopabf 4191 ralrnmpt 5555 rexrnmpt 5556 dfopab2 6080 dfoprab3s 6081 mpoxopoveq 6130 |
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