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Mirrors > Home > ILE Home > Th. List > opelxpd | Unicode version |
Description: Ordered pair membership in a Cartesian product, deduction form. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
Ref | Expression |
---|---|
opelxpd.1 | |
opelxpd.2 |
Ref | Expression |
---|---|
opelxpd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpd.1 | . 2 | |
2 | opelxpd.2 | . 2 | |
3 | opelxpi 4571 | . 2 | |
4 | 1, 2, 3 | syl2anc 408 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cop 3530 cxp 4537 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 |
This theorem is referenced by: suplocsrlemb 7614 seqvalcd 10232 ctiunctlemfo 11952 strslfv2d 12001 txcnp 12440 upxp 12441 txcnmpt 12442 uptx 12443 txdis1cn 12447 txlm 12448 lmcn2 12449 txhmeo 12488 comet 12668 txmetcnp 12687 dvaddxxbr 12834 dvmulxxbr 12835 dvcoapbr 12840 |
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