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Mirrors > Home > MPE Home > Th. List > abid2f | Unicode version |
Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 5-Sep-2011.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 17-Nov-2019.) |
Ref | Expression |
---|---|
abid2f.1 |
Ref | Expression |
---|---|
abid2f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfab1 2621 | . . 3 | |
2 | abid2f.1 | . . 3 | |
3 | 1, 2 | cleqf 2646 | . 2 |
4 | abid 2444 | . 2 | |
5 | 3, 4 | mpgbir 1622 | 1 |
Colors of variables: wff setvar class |
Syntax hints: <-> wb 184 = wceq 1395
e. wcel 1818 { cab 2442 F/_ wnfc 2605 |
This theorem is referenced by: mptctf 27544 rabexgf 31399 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 |
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