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Mirrors > Home > ILE Home > Th. List > xpeq2 | Unicode version |
Description: Equality theorem for cross product. (Contributed by NM, 5-Jul-1994.) |
Ref | Expression |
---|---|
xpeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2142 | . . . 4 | |
2 | 1 | anbi2d 451 | . . 3 |
3 | 2 | opabbidv 3844 | . 2 |
4 | df-xp 4369 | . 2 | |
5 | df-xp 4369 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 copab 3838 cxp 4361 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-opab 3840 df-xp 4369 |
This theorem is referenced by: xpeq12 4382 xpeq2i 4384 xpeq2d 4387 xpeq0r 4766 xpdisj2 4768 xpcomeng 6325 |
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