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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 3279 |
. 2
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2 | df-pr 3598 |
. 2
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3 | df-pr 3598 |
. 2
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4 | 1, 2, 3 | 3eqtr4i 2208 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-pr 3598 |
This theorem is referenced by: preq2 3669 tpcoma 3685 tpidm23 3692 prid2g 3696 prid2 3698 prprc2 3700 difprsn2 3731 preqr2g 3765 preqr2 3767 preq12b 3768 fvpr2 5717 fvpr2g 5719 en2other2 7189 maxcom 11193 mincom 11218 xrmax2sup 11243 xrmaxltsup 11247 xrmaxadd 11250 xrbdtri 11265 qtopbasss 13685 |
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