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Mirrors > Home > ILE Home > Th. List > prneli | Unicode version |
Description: If an element doesn't
match the items in an unordered pair, it is not in
the unordered pair, using ![]() |
Ref | Expression |
---|---|
prneli.1 |
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prneli.2 |
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Ref | Expression |
---|---|
prneli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prneli.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | prneli.2 |
. . 3
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3 | 1, 2 | nelpri 3631 |
. 2
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4 | 3 | nelir 2458 |
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 615 ax-in2 616 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-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 |
This theorem is referenced by: (None) |
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