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Mirrors > Home > ILE Home > Th. List > preq2 | Unicode version |
Description: Equality theorem for unordered pairs. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
preq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3608 |
. 2
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2 | prcom 3607 |
. 2
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3 | prcom 3607 |
. 2
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4 | 1, 2, 3 | 3eqtr4g 2198 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 |
This theorem is referenced by: preq12 3610 preq2i 3612 preq2d 3615 tpeq2 3618 preq12bg 3708 opeq2 3714 uniprg 3759 intprg 3812 prexg 4141 opth 4167 opeqsn 4182 relop 4697 funopg 5165 pr2ne 7065 hashprg 10586 bj-prexg 13280 |
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