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Mirrors > Home > ILE Home > Th. List > preq1 | Unicode version |
Description: Equality theorem for unordered pairs. (Contributed by NM, 29-Mar-1998.) |
Ref | Expression |
---|---|
preq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3618 |
. . 3
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2 | 1 | uneq1d 3303 |
. 2
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3 | df-pr 3614 |
. 2
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4 | df-pr 3614 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2247 |
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-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 |
This theorem is referenced by: preq2 3685 preq12 3686 preq1i 3687 preq1d 3690 tpeq1 3693 prnzg 3731 preq12b 3785 preq12bg 3788 opeq1 3793 uniprg 3839 intprg 3892 prexg 4226 opthreg 4570 bdxmet 14398 bj-prexg 15060 |
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