![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 1401 | . . 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 2965 | . 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵) |
7 | 6 | mptru 1299 | 1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑦⦌𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1291 Ⅎwnfc 2216 ⦋csb 2934 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-sbc 2842 df-csb 2935 |
This theorem is referenced by: cbvralcsf 2991 cbvrexcsf 2992 cbvreucsf 2993 cbvrabcsf 2994 fmptcof 5479 mpt2mptsx 5981 dmmpt2ssx 5983 fmpt2x 5984 fmpt2co 5995 dfmpt2 6002 f1od2 6014 nfsum 10807 fsum2dlemstep 10889 fisumcom2 10893 |
Copyright terms: Public domain | W3C validator |