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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2253 |
. . . 4
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2 | 1 | anbi2d 464 |
. . 3
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3 | 2 | opabbidv 4087 |
. 2
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4 | df-xp 4653 |
. 2
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5 | df-xp 4653 |
. 2
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6 | 3, 4, 5 | 3eqtr4g 2247 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-opab 4083 df-xp 4653 |
This theorem is referenced by: xpeq12 4666 xpeq2i 4668 xpeq2d 4671 xpeq0r 5072 xpdisj2 5075 pmvalg 6689 xpcomeng 6858 djueq12 7072 txuni2 14241 txbas 14243 txopn 14250 txrest 14261 txdis 14262 txdis1cn 14263 xmettxlem 14494 xmettx 14495 |
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