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Mirrors > Home > ILE Home > Th. List > cbviota | Unicode version |
Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.) |
Ref | Expression |
---|---|
cbviota.1 | |
cbviota.2 | |
cbviota.3 |
Ref | Expression |
---|---|
cbviota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1515 | . . . . . 6 | |
2 | nfs1v 1926 | . . . . . . 7 | |
3 | nfv 1515 | . . . . . . 7 | |
4 | 2, 3 | nfbi 1576 | . . . . . 6 |
5 | sbequ12 1758 | . . . . . . 7 | |
6 | equequ1 1699 | . . . . . . 7 | |
7 | 5, 6 | bibi12d 234 | . . . . . 6 |
8 | 1, 4, 7 | cbval 1741 | . . . . 5 |
9 | cbviota.2 | . . . . . . . 8 | |
10 | 9 | nfsb 1933 | . . . . . . 7 |
11 | nfv 1515 | . . . . . . 7 | |
12 | 10, 11 | nfbi 1576 | . . . . . 6 |
13 | nfv 1515 | . . . . . 6 | |
14 | sbequ 1827 | . . . . . . . 8 | |
15 | cbviota.3 | . . . . . . . . 9 | |
16 | cbviota.1 | . . . . . . . . 9 | |
17 | 15, 16 | sbie 1778 | . . . . . . . 8 |
18 | 14, 17 | bitrdi 195 | . . . . . . 7 |
19 | equequ1 1699 | . . . . . . 7 | |
20 | 18, 19 | bibi12d 234 | . . . . . 6 |
21 | 12, 13, 20 | cbval 1741 | . . . . 5 |
22 | 8, 21 | bitri 183 | . . . 4 |
23 | 22 | abbii 2280 | . . 3 |
24 | 23 | unieqi 3793 | . 2 |
25 | dfiota2 5148 | . 2 | |
26 | dfiota2 5148 | . 2 | |
27 | 24, 25, 26 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 wnf 1447 wsb 1749 cab 2150 cuni 3783 cio 5145 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-sn 3576 df-uni 3784 df-iota 5147 |
This theorem is referenced by: cbviotav 5153 cbvriota 5802 |
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