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Mirrors > Home > MPE Home > Th. List > preq12i | Structured version Unicode version |
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.) |
Ref | Expression |
---|---|
preq1i.1 |
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preq12i.2 |
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Ref | Expression |
---|---|
preq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1i.1 |
. 2
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2 | preq12i.2 |
. 2
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3 | preq12 4067 |
. 2
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4 | 1, 2, 3 | mp2an 672 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-v 3080 df-un 3444 df-sn 3989 df-pr 3991 |
This theorem is referenced by: grpbasex 14404 grpplusgx 14405 indistpsx 18756 lgsdir2lem5 22809 wlkntrllem2 23638 clwwlkgt0 30605 zlmodzxzadd 30926 zlmodzxzequa 31193 zlmodzxzequap 31196 tgrpset 34752 |
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