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Mirrors > Home > MPE Home > Th. List > ax12wdemo | Structured version Visualization version Unicode version |
Description: Example of an application of ax12w 2010 that results in an instance of ax-12 2047 for a contrived formula with mixed free and bound variables, , in place of . The proof illustrates bound variable renaming with cbvalvw 1969 to obtain fresh variables to avoid distinct variable clashes. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 14-Apr-2017.) |
Ref | Expression |
---|---|
ax12wdemo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ1 1997 | . . 3 | |
2 | elequ2 2004 | . . . . 5 | |
3 | 2 | cbvalvw 1969 | . . . 4 |
4 | 3 | a1i 11 | . . 3 |
5 | elequ1 1997 | . . . . . 6 | |
6 | 5 | albidv 1849 | . . . . 5 |
7 | 6 | cbvalvw 1969 | . . . 4 |
8 | elequ2 2004 | . . . . . 6 | |
9 | 8 | albidv 1849 | . . . . 5 |
10 | 9 | albidv 1849 | . . . 4 |
11 | 7, 10 | syl5bb 272 | . . 3 |
12 | 1, 4, 11 | 3anbi123d 1399 | . 2 |
13 | elequ2 2004 | . . 3 | |
14 | 7 | a1i 11 | . . 3 |
15 | 13, 14 | 3anbi13d 1401 | . 2 |
16 | 12, 15 | ax12w 2010 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 w3a 1037 wal 1481 |
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-8 1992 ax-9 1999 |
This theorem depends on definitions: df-bi 197 df-an 386 df-3an 1039 df-ex 1705 |
This theorem is referenced by: (None) |
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