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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 3215 | . 2 | |
2 | df-pr 3529 | . 2 | |
3 | df-pr 3529 | . 2 | |
4 | 1, 2, 3 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cun 3064 csn 3522 cpr 3523 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-pr 3529 |
This theorem is referenced by: preq2 3596 tpcoma 3612 tpidm23 3619 prid2g 3623 prid2 3625 prprc2 3627 difprsn2 3655 preqr2g 3689 preqr2 3691 preq12b 3692 fvpr2 5618 fvpr2g 5620 en2other2 7045 maxcom 10968 mincom 10993 xrmax2sup 11016 xrmaxltsup 11020 xrmaxadd 11023 xrbdtri 11038 qtopbasss 12679 |
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