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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 2234 | . . . 4 | |
2 | 1 | anbi2d 461 | . . 3 |
3 | 2 | opabbidv 4053 | . 2 |
4 | df-xp 4615 | . 2 | |
5 | df-xp 4615 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 copab 4047 cxp 4607 |
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-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-opab 4049 df-xp 4615 |
This theorem is referenced by: xpeq12 4628 xpeq2i 4630 xpeq2d 4633 xpeq0r 5031 xpdisj2 5034 pmvalg 6634 xpcomeng 6803 djueq12 7013 txuni2 13011 txbas 13013 txopn 13020 txrest 13031 txdis 13032 txdis1cn 13033 xmettxlem 13264 xmettx 13265 |
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