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Mirrors > Home > ILE Home > Th. List > xpima1 | Unicode version |
Description: The image by a cross product. (Contributed by Thierry Arnoux, 16-Dec-2017.) |
Ref | Expression |
---|---|
xpima1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 4635 |
. . 3
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2 | df-res 4634 |
. . . 4
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3 | 2 | rneqi 4850 |
. . 3
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4 | inxp 4756 |
. . . 4
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5 | 4 | rneqi 4850 |
. . 3
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6 | 1, 3, 5 | 3eqtri 2202 |
. 2
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7 | xpeq1 4636 |
. . . 4
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8 | 0xp 4702 |
. . . 4
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9 | 7, 8 | eqtrdi 2226 |
. . 3
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10 | rneq 4849 |
. . . 4
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11 | rn0 4878 |
. . . 4
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12 | 10, 11 | eqtrdi 2226 |
. . 3
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13 | 9, 12 | syl 14 |
. 2
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14 | 6, 13 | eqtrid 2222 |
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-in1 614 ax-in2 615 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 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-xp 4628 df-rel 4629 df-cnv 4630 df-dm 4632 df-rn 4633 df-res 4634 df-ima 4635 |
This theorem is referenced by: (None) |
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