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Mirrors > Home > NFE Home > Th. List > spc2egv | Unicode version |
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.) |
Ref | Expression |
---|---|
spc2egv.1 |
Ref | Expression |
---|---|
spc2egv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2869 | . . . 4 | |
2 | elisset 2869 | . . . 4 | |
3 | 1, 2 | anim12i 549 | . . 3 |
4 | eeanv 1913 | . . 3 | |
5 | 3, 4 | sylibr 203 | . 2 |
6 | spc2egv.1 | . . . 4 | |
7 | 6 | biimprcd 216 | . . 3 |
8 | 7 | 2eximdv 1624 | . 2 |
9 | 5, 8 | syl5com 26 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: spc2gv 2942 spc2ev 2947 |
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