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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 4630 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 cop 3573 cxp 4596 |
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-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-opab 4038 df-xp 4604 |
This theorem is referenced by: suplocsrlemb 7738 seqvalcd 10384 ctiunctlemfo 12315 strslfv2d 12379 txcnp 12818 upxp 12819 txcnmpt 12820 uptx 12821 txdis1cn 12825 txlm 12826 lmcn2 12827 txhmeo 12866 comet 13046 txmetcnp 13065 dvaddxxbr 13212 dvmulxxbr 13213 dvcoapbr 13218 |
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