Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sb56 | Unicode version |
Description: Two equivalent ways of expressing the proper substitution of for in , when and are distinct. Theorem 6.2 of [Quine] p. 40. The proof does not involve df-sb 1646. (Contributed by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb56 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1433 | . 2 | |
2 | ax11v 1708 | . . 3 | |
3 | ax-4 1400 | . . . 4 | |
4 | 3 | com12 27 | . . 3 |
5 | 2, 4 | impbid 120 | . 2 |
6 | 1, 5 | equsex 1616 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: sb6 1766 sb5 1767 alexeq 2670 |
Copyright terms: Public domain | W3C validator |