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Mirrors > Home > NFE Home > Th. List > rr19.28v | Unicode version |
Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. We don't need the nonempty class condition of r19.28zv 3645 when there is an outer quantifier. (Contributed by NM, 29-Oct-2012.) |
Ref | Expression |
---|---|
rr19.28v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . . . . . 6 | |
2 | 1 | ralimi 2689 | . . . . 5 |
3 | biidd 228 | . . . . . 6 | |
4 | 3 | rspcv 2951 | . . . . 5 |
5 | 2, 4 | syl5 28 | . . . 4 |
6 | simpr 447 | . . . . . 6 | |
7 | 6 | ralimi 2689 | . . . . 5 |
8 | 7 | a1i 10 | . . . 4 |
9 | 5, 8 | jcad 519 | . . 3 |
10 | 9 | ralimia 2687 | . 2 |
11 | r19.28av 2753 | . . 3 | |
12 | 11 | ralimi 2689 | . 2 |
13 | 10, 12 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wceq 1642 wcel 1710 wral 2614 |
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-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 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-ral 2619 df-v 2861 |
This theorem is referenced by: (None) |
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