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Mirrors > Home > ILE Home > Th. List > opelxpi | Unicode version |
Description: Ordered pair membership in a cross product (implication). (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
opelxpi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp 4467 |
. 2
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2 | 1 | biimpri 131 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-opab 3900 df-xp 4444 |
This theorem is referenced by: opelxpd 4470 opelvvg 4487 opelvv 4488 opbrop 4517 fliftrel 5571 fnotovb 5692 ovi3 5781 ovres 5784 fovrn 5787 fnovrn 5792 ovconst2 5796 oprab2co 5983 1stconst 5986 2ndconst 5987 f1od2 6000 brdifun 6319 ecopqsi 6347 brecop 6382 th3q 6397 xpcomco 6542 xpf1o 6560 xpmapenlem 6565 djulclr 6741 djurclr 6742 djulcl 6743 djurcl 6744 djuf1olem 6745 addpiord 6875 mulpiord 6876 enqeceq 6918 1nq 6925 addpipqqslem 6928 mulpipq 6931 mulpipqqs 6932 addclnq 6934 mulclnq 6935 recexnq 6949 ltexnqq 6967 prarloclemarch 6977 prarloclemarch2 6978 nnnq 6981 enq0breq 6995 enq0eceq 6996 nqnq0 7000 addnnnq0 7008 mulnnnq0 7009 addclnq0 7010 mulclnq0 7011 nqpnq0nq 7012 prarloclemlt 7052 prarloclemlo 7053 prarloclemcalc 7061 genpelxp 7070 nqprm 7101 ltexprlempr 7167 recexprlempr 7191 cauappcvgprlemcl 7212 cauappcvgprlemladd 7217 caucvgprlemcl 7235 caucvgprprlemcl 7263 enreceq 7282 addsrpr 7291 mulsrpr 7292 0r 7296 1sr 7297 m1r 7298 addclsr 7299 mulclsr 7300 prsrcl 7329 addcnsr 7371 mulcnsr 7372 addcnsrec 7379 mulcnsrec 7380 pitonnlem2 7384 pitonn 7385 pitore 7387 recnnre 7388 axaddcl 7401 axmulcl 7403 xrlenlt 7551 frecuzrdgg 9823 frecuzrdgsuctlem 9830 iseqvalt 9873 seq3val 9874 cnrecnv 10344 eucalgf 11315 eucialg 11319 qredeu 11357 qnumdenbi 11448 crth 11478 phimullem 11479 setscom 11534 setsslid 11544 djucllem 11700 |
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