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Mirrors > Home > ILE Home > Th. List > prcom | Unicode version |
Description: Commutative law for unordered pairs. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
prcom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 3128 |
. 2
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2 | df-pr 3429 |
. 2
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3 | df-pr 3429 |
. 2
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4 | 1, 2, 3 | 3eqtr4i 2113 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2614 df-un 2988 df-pr 3429 |
This theorem is referenced by: preq2 3494 tpcoma 3510 tpidm23 3517 prid2g 3521 prid2 3523 prprc2 3525 difprsn2 3551 preqr2g 3585 preqr2 3587 preq12b 3588 fvpr2 5442 fvpr2g 5444 en2other2 6725 maxcom 10463 mincom 10485 |
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