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Mirrors > Home > ILE Home > Th. List > hbequid | Unicode version |
Description: Bound-variable hypothesis builder for . This theorem tells us that any variable, including , is effectively not free in , even though is technically free according to the traditional definition of free variable. (The proof uses only ax-5 1423, ax-8 1482, ax-12 1489, and ax-gen 1425. This shows that this can be proved without ax-9 1511, even though the theorem equid 1677 cannot be. A shorter proof using ax-9 1511 is obtainable from equid 1677 and hbth 1439.) (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 23-Mar-2014.) |
Ref | Expression |
---|---|
hbequid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12or 1490 | . 2 | |
2 | ax-8 1482 | . . . . . 6 | |
3 | 2 | pm2.43i 49 | . . . . 5 |
4 | 3 | alimi 1431 | . . . 4 |
5 | 4 | a1d 22 | . . 3 |
6 | ax-4 1487 | . . . 4 | |
7 | 5, 6 | jaoi 705 | . . 3 |
8 | 5, 7 | jaoi 705 | . 2 |
9 | 1, 8 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 697 wal 1329 wceq 1331 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-gen 1425 ax-8 1482 ax-i12 1485 ax-4 1487 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: equveli 1732 |
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