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Mirrors > Home > ILE Home > Th. List > rspc2ev | Unicode version |
Description: 2-variable restricted existential specialization, using implicit substitution. (Contributed by NM, 16-Oct-1999.) |
Ref | Expression |
---|---|
rspc2v.1 |
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rspc2v.2 |
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Ref | Expression |
---|---|
rspc2ev |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc2v.2 |
. . . . 5
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2 | 1 | rspcev 2760 |
. . . 4
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3 | 2 | anim2i 337 |
. . 3
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4 | 3 | 3impb 1160 |
. 2
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5 | rspc2v.1 |
. . . 4
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6 | 5 | rexbidv 2412 |
. . 3
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7 | 6 | rspcev 2760 |
. 2
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8 | 4, 7 | syl 14 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-v 2659 |
This theorem is referenced by: rspc3ev 2776 opelxp 4529 rspceov 5767 2dom 6653 apreim 8283 addcn2 10971 mulcn2 10973 divalglemnn 11463 bezoutlema 11533 bezoutlemb 11534 txuni2 12267 txopn 12276 txdis 12288 txdis1cn 12289 xmettxlem 12498 |
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