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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 1442 | . . 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 3036 | . 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵) |
7 | 6 | mptru 1340 | 1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1332 Ⅎwnfc 2268 ⦋csb 3003 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: cbvralcsf 3062 cbvrexcsf 3063 cbvreucsf 3064 cbvrabcsf 3065 elfvmptrab1 5515 fmptcof 5587 mpomptsx 6095 dmmpossx 6097 fmpox 6098 fmpoco 6113 dfmpo 6120 f1od2 6132 nfsum 11126 fsum2dlemstep 11203 fisumcom2 11207 nfcprod 11324 fsumcncntop 12725 |
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