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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 3504 |
. . 3
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2 | 1 | uneq1d 3195 |
. 2
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3 | df-pr 3500 |
. 2
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4 | df-pr 3500 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2172 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-sn 3499 df-pr 3500 |
This theorem is referenced by: preq2 3567 preq12 3568 preq1i 3569 preq1d 3572 tpeq1 3575 prnzg 3613 preq12b 3663 preq12bg 3666 opeq1 3671 uniprg 3717 intprg 3770 prexg 4093 opthreg 4431 bdxmet 12490 bj-prexg 12801 |
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