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Mirrors > Home > ILE Home > Th. List > cbviun | Unicode version |
Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 26-Mar-2006.) (Revised by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
cbviun.1 | |
cbviun.2 | |
cbviun.3 |
Ref | Expression |
---|---|
cbviun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbviun.1 | . . . . 5 | |
2 | 1 | nfcri 2293 | . . . 4 |
3 | cbviun.2 | . . . . 5 | |
4 | 3 | nfcri 2293 | . . . 4 |
5 | cbviun.3 | . . . . 5 | |
6 | 5 | eleq2d 2227 | . . . 4 |
7 | 2, 4, 6 | cbvrex 2677 | . . 3 |
8 | 7 | abbii 2273 | . 2 |
9 | df-iun 3851 | . 2 | |
10 | df-iun 3851 | . 2 | |
11 | 8, 9, 10 | 3eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 cab 2143 wnfc 2286 wrex 2436 ciun 3849 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-iun 3851 |
This theorem is referenced by: cbviunv 3888 funiunfvdmf 5714 mpomptsx 6145 dmmpossx 6147 fmpox 6148 fsum2dlemstep 11331 fisumcom2 11335 fsumiun 11374 fprod2dlemstep 11519 fprodcom2fi 11523 ctiunctlemf 12167 ctiunctal 12170 |
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