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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 5534 |
. . . 4
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2 | isms.j |
. . . 4
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3 | 1, 2 | eqtr4di 2240 |
. . 3
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4 | fveq2 5534 |
. . . . . 6
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5 | fveq2 5534 |
. . . . . . . 8
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6 | isms.x |
. . . . . . . 8
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7 | 5, 6 | eqtr4di 2240 |
. . . . . . 7
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8 | 7 | sqxpeqd 4670 |
. . . . . 6
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9 | 4, 8 | reseq12d 4926 |
. . . . 5
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10 | isms.d |
. . . . 5
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11 | 9, 10 | eqtr4di 2240 |
. . . 4
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12 | 11 | fveq2d 5538 |
. . 3
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13 | 3, 12 | eqeq12d 2204 |
. 2
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14 | df-xms 14291 |
. 2
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15 | 13, 14 | elrab2 2911 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 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-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4650 df-res 4656 df-iota 5196 df-fv 5243 df-xms 14291 |
This theorem is referenced by: isxms2 14404 xmstopn 14407 xmstps 14409 xmspropd 14429 |
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