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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 3261 | . 2 | |
2 | df-pr 3577 | . 2 | |
3 | df-pr 3577 | . 2 | |
4 | 1, 2, 3 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 cun 3109 csn 3570 cpr 3571 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-pr 3577 |
This theorem is referenced by: preq2 3648 tpcoma 3664 tpidm23 3671 prid2g 3675 prid2 3677 prprc2 3679 difprsn2 3707 preqr2g 3741 preqr2 3743 preq12b 3744 fvpr2 5684 fvpr2g 5686 en2other2 7143 maxcom 11131 mincom 11156 xrmax2sup 11181 xrmaxltsup 11185 xrmaxadd 11188 xrbdtri 11203 qtopbasss 13068 |
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