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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 | |
rspc2v.2 |
Ref | Expression |
---|---|
rspc2ev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc2v.2 | . . . . 5 | |
2 | 1 | rspcev 2763 | . . . 4 |
3 | 2 | anim2i 339 | . . 3 |
4 | 3 | 3impb 1162 | . 2 |
5 | rspc2v.1 | . . . 4 | |
6 | 5 | rexbidv 2415 | . . 3 |
7 | 6 | rspcev 2763 | . 2 |
8 | 4, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 947 wceq 1316 wcel 1465 wrex 2394 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 |
This theorem is referenced by: rspc3ev 2780 opelxp 4539 rspceov 5781 2dom 6667 apreim 8333 addcn2 11047 mulcn2 11049 divalglemnn 11542 bezoutlema 11614 bezoutlemb 11615 txuni2 12352 txopn 12361 txdis 12373 txdis1cn 12374 xmettxlem 12605 |
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