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Mirrors > Home > NFE 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 2955 | . . . 4 |
3 | 2 | anim2i 552 | . . 3 |
4 | 3 | 3impb 1147 | . 2 |
5 | rspc2v.1 | . . . 4 | |
6 | 5 | rexbidv 2635 | . . 3 |
7 | 6 | rspcev 2955 | . 2 |
8 | 4, 7 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wceq 1642 wcel 1710 wrex 2615 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 |
This theorem is referenced by: rspc3ev 2965 eladdci 4399 rspceov 5556 nclec 6195 ltcpw1pwg 6202 nc0le1 6216 nclenc 6222 ce2le 6233 tlenc1c 6240 |
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