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Mirrors > Home > ILE Home > Th. List > inxp | Unicode version |
Description: The intersection of two cross products. Exercise 9 of [TakeutiZaring] p. 25. (Contributed by NM, 3-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
inxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inopab 4759 |
. . 3
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2 | an4 586 |
. . . . 5
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3 | elin 3318 |
. . . . . 6
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4 | elin 3318 |
. . . . . 6
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5 | 3, 4 | anbi12i 460 |
. . . . 5
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6 | 2, 5 | bitr4i 187 |
. . . 4
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7 | 6 | opabbii 4070 |
. . 3
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8 | 1, 7 | eqtri 2198 |
. 2
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9 | df-xp 4632 |
. . 3
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10 | df-xp 4632 |
. . 3
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11 | 9, 10 | ineq12i 3334 |
. 2
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12 | df-xp 4632 |
. 2
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13 | 8, 11, 12 | 3eqtr4i 2208 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-opab 4065 df-xp 4632 df-rel 4633 |
This theorem is referenced by: xpindi 4762 xpindir 4763 dmxpin 4849 xpssres 4942 xpdisj1 5053 xpdisj2 5054 imainrect 5074 xpima1 5075 xpima2m 5076 hashxp 10801 txbas 13651 txrest 13669 metreslem 13773 |
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