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Mirrors > Home > MPE Home > Th. List > eqvincf | Structured version Visualization version Unicode version |
Description: A variable introduction law for class equality, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 14-Sep-2003.) |
Ref | Expression |
---|---|
eqvincf.1 | |
eqvincf.2 | |
eqvincf.3 |
Ref | Expression |
---|---|
eqvincf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvincf.3 | . . 3 | |
2 | 1 | eqvinc 3330 | . 2 |
3 | eqvincf.1 | . . . . 5 | |
4 | 3 | nfeq2 2780 | . . . 4 |
5 | eqvincf.2 | . . . . 5 | |
6 | 5 | nfeq2 2780 | . . . 4 |
7 | 4, 6 | nfan 1828 | . . 3 |
8 | nfv 1843 | . . 3 | |
9 | eqeq1 2626 | . . . 4 | |
10 | eqeq1 2626 | . . . 4 | |
11 | 9, 10 | anbi12d 747 | . . 3 |
12 | 7, 8, 11 | cbvex 2272 | . 2 |
13 | 2, 12 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 wnfc 2751 cvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 |
This theorem is referenced by: (None) |
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