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Mirrors > Home > ILE Home > Th. List > cbvixp | Unicode version |
Description: Change bound variable in an indexed Cartesian product. (Contributed by Jeff Madsen, 20-Jun-2011.) |
Ref | Expression |
---|---|
cbvixp.1 | |
cbvixp.2 | |
cbvixp.3 |
Ref | Expression |
---|---|
cbvixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvixp.1 | . . . . . 6 | |
2 | 1 | nfel2 2319 | . . . . 5 |
3 | cbvixp.2 | . . . . . 6 | |
4 | 3 | nfel2 2319 | . . . . 5 |
5 | fveq2 5480 | . . . . . 6 | |
6 | cbvixp.3 | . . . . . 6 | |
7 | 5, 6 | eleq12d 2235 | . . . . 5 |
8 | 2, 4, 7 | cbvral 2685 | . . . 4 |
9 | 8 | anbi2i 453 | . . 3 |
10 | 9 | abbii 2280 | . 2 |
11 | dfixp 6657 | . 2 | |
12 | dfixp 6657 | . 2 | |
13 | 10, 11, 12 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 cab 2150 wnfc 2293 wral 2442 wfn 5177 cfv 5182 cixp 6655 |
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-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-iota 5147 df-fn 5185 df-fv 5190 df-ixp 6656 |
This theorem is referenced by: cbvixpv 6673 mptelixpg 6691 |
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