Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ixpeq1 | Unicode version |
Description: Equality theorem for infinite Cartesian product. (Contributed by NM, 29-Sep-2006.) |
Ref | Expression |
---|---|
ixpeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq2 5271 | . . . 4 | |
2 | raleq 2659 | . . . 4 | |
3 | 1, 2 | anbi12d 465 | . . 3 |
4 | 3 | abbidv 2282 | . 2 |
5 | dfixp 6657 | . 2 | |
6 | dfixp 6657 | . 2 | |
7 | 4, 5, 6 | 3eqtr4g 2222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 cab 2150 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-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-fn 5185 df-ixp 6656 |
This theorem is referenced by: ixpeq1d 6667 |
Copyright terms: Public domain | W3C validator |