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Mirrors > Home > ILE Home > Th. List > iota2 | Unicode version |
Description: The unique element such
that ![]() |
Ref | Expression |
---|---|
iota2.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
iota2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2763 |
. 2
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2 | simpl 109 |
. . 3
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3 | simpr 110 |
. . 3
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4 | iota2.1 |
. . . 4
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5 | 4 | adantl 277 |
. . 3
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6 | nfv 1539 |
. . . 4
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7 | nfeu1 2049 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | nfan 1576 |
. . 3
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9 | nfvd 1540 |
. . 3
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10 | nfcvd 2333 |
. . 3
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11 | 2, 3, 5, 8, 9, 10 | iota2df 5224 |
. 2
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12 | 1, 11 | sylan 283 |
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-eu 2041 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-sn 3616 df-pr 3617 df-uni 3828 df-iota 5199 |
This theorem is referenced by: iotam 5230 pczpre 12340 pcdiv 12345 gsum0g 12882 gsumval2 12883 |
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