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Mirrors > Home > ILE Home > Th. List > cbvralfw | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Version of cbvralf 2682 with a disjoint variable condition. Although we don't do so yet, we expect this disjoint variable condition will allow us to remove reliance on ax-i12 1494 and ax-bndl 1496 in the proof. (Contributed by NM, 7-Mar-2004.) (Revised by Gino Giotto, 23-May-2024.) |
Ref | Expression |
---|---|
cbvralfw.1 | |
cbvralfw.2 | |
cbvralfw.3 | |
cbvralfw.4 | |
cbvralfw.5 |
Ref | Expression |
---|---|
cbvralfw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralfw.2 | . . . . 5 | |
2 | 1 | nfcri 2300 | . . . 4 |
3 | cbvralfw.3 | . . . 4 | |
4 | 2, 3 | nfim 1559 | . . 3 |
5 | cbvralfw.1 | . . . . 5 | |
6 | 5 | nfcri 2300 | . . . 4 |
7 | cbvralfw.4 | . . . 4 | |
8 | 6, 7 | nfim 1559 | . . 3 |
9 | eleq1w 2225 | . . . 4 | |
10 | cbvralfw.5 | . . . 4 | |
11 | 9, 10 | imbi12d 233 | . . 3 |
12 | 4, 8, 11 | cbvalv1 1738 | . 2 |
13 | df-ral 2447 | . 2 | |
14 | df-ral 2447 | . 2 | |
15 | 12, 13, 14 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wnf 1447 wcel 2135 wnfc 2293 wral 2442 |
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-nf 1448 df-sb 1750 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 |
This theorem is referenced by: cbvralw 2684 |
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