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Mirrors > Home > ILE Home > Th. List > cbvralf | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 7-Mar-2004.) (Revised by Mario Carneiro, 9-Oct-2016.) |
Ref | Expression |
---|---|
cbvralf.1 | |
cbvralf.2 | |
cbvralf.3 | |
cbvralf.4 | |
cbvralf.5 |
Ref | Expression |
---|---|
cbvralf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . 4 | |
2 | cbvralf.1 | . . . . . 6 | |
3 | 2 | nfcri 2273 | . . . . 5 |
4 | nfs1v 1910 | . . . . 5 | |
5 | 3, 4 | nfim 1551 | . . . 4 |
6 | eleq1 2200 | . . . . 5 | |
7 | sbequ12 1744 | . . . . 5 | |
8 | 6, 7 | imbi12d 233 | . . . 4 |
9 | 1, 5, 8 | cbval 1727 | . . 3 |
10 | cbvralf.2 | . . . . . 6 | |
11 | 10 | nfcri 2273 | . . . . 5 |
12 | cbvralf.3 | . . . . . 6 | |
13 | 12 | nfsb 1917 | . . . . 5 |
14 | 11, 13 | nfim 1551 | . . . 4 |
15 | nfv 1508 | . . . 4 | |
16 | eleq1 2200 | . . . . 5 | |
17 | sbequ 1812 | . . . . . 6 | |
18 | cbvralf.4 | . . . . . . 7 | |
19 | cbvralf.5 | . . . . . . 7 | |
20 | 18, 19 | sbie 1764 | . . . . . 6 |
21 | 17, 20 | syl6bb 195 | . . . . 5 |
22 | 16, 21 | imbi12d 233 | . . . 4 |
23 | 14, 15, 22 | cbval 1727 | . . 3 |
24 | 9, 23 | bitri 183 | . 2 |
25 | df-ral 2419 | . 2 | |
26 | df-ral 2419 | . 2 | |
27 | 24, 25, 26 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wnf 1436 wcel 1480 wsb 1735 wnfc 2266 wral 2414 |
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-nf 1437 df-sb 1736 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 |
This theorem is referenced by: cbvral 2648 ffnfvf 5572 |
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