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Mirrors > Home > ILE Home > Th. List > nfcsb | GIF version |
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfcsb.1 | ⊢ Ⅎ𝑥𝐴 |
nfcsb.2 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfcsb | ⊢ Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1443 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfcsb.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
4 | nfcsb.2 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
5 | 4 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
6 | 1, 3, 5 | nfcsbd 3041 | . 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵) |
7 | 6 | mptru 1341 | 1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1333 Ⅎwnfc 2269 ⦋csb 3007 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-sbc 2914 df-csb 3008 |
This theorem is referenced by: cbvralcsf 3067 cbvrexcsf 3068 cbvreucsf 3069 cbvrabcsf 3070 elfvmptrab1 5523 fmptcof 5595 mpomptsx 6103 dmmpossx 6105 fmpox 6106 fmpoco 6121 dfmpo 6128 f1od2 6140 nfsum 11158 fsum2dlemstep 11235 fisumcom2 11239 nfcprod 11356 fsumcncntop 12764 |
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