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Mirrors > Home > ILE Home > Th. List > isxms | Unicode version |
Description: Express the predicate
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Ref | Expression |
---|---|
isms.j |
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isms.x |
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isms.d |
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Ref | Expression |
---|---|
isxms |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 5429 |
. . . 4
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2 | isms.j |
. . . 4
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3 | 1, 2 | eqtr4di 2191 |
. . 3
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4 | fveq2 5429 |
. . . . . 6
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5 | fveq2 5429 |
. . . . . . . 8
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6 | isms.x |
. . . . . . . 8
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7 | 5, 6 | eqtr4di 2191 |
. . . . . . 7
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8 | 7 | sqxpeqd 4573 |
. . . . . 6
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9 | 4, 8 | reseq12d 4828 |
. . . . 5
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10 | isms.d |
. . . . 5
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11 | 9, 10 | eqtr4di 2191 |
. . . 4
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12 | 11 | fveq2d 5433 |
. . 3
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13 | 3, 12 | eqeq12d 2155 |
. 2
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14 | df-xms 12547 |
. 2
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15 | 13, 14 | elrab2 2847 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-rab 2426 df-v 2691 df-un 3080 df-in 3082 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-res 4559 df-iota 5096 df-fv 5139 df-xms 12547 |
This theorem is referenced by: isxms2 12660 xmstopn 12663 xmstps 12665 xmspropd 12685 |
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