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Mirrors > Home > NFE Home > Th. List > elabgf | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
elabgf.1 | |
elabgf.2 | |
elabgf.3 |
Ref | Expression |
---|---|
elabgf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elabgf.1 | . 2 | |
2 | nfab1 2491 | . . . 4 | |
3 | 1, 2 | nfel 2497 | . . 3 |
4 | elabgf.2 | . . 3 | |
5 | 3, 4 | nfbi 1834 | . 2 |
6 | eleq1 2413 | . . 3 | |
7 | elabgf.3 | . . 3 | |
8 | 6, 7 | bibi12d 312 | . 2 |
9 | abid 2341 | . 2 | |
10 | 1, 5, 8, 9 | vtoclgf 2913 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wnf 1544 wceq 1642 wcel 1710 cab 2339 wnfc 2476 |
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-v 2861 |
This theorem is referenced by: elabf 2984 elabg 2986 elab3gf 2990 elrabf 2993 |
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