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Mirrors > Home > ILE Home > Th. List > sbft | Unicode version |
Description: Substitution has no effect on a non-free variable. (Contributed by NM, 30-May-2009.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 3-May-2018.) |
Ref | Expression |
---|---|
sbft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spsbe 1723 | . . 3 | |
2 | 19.9t 1533 | . . 3 | |
3 | 1, 2 | syl5ib 143 | . 2 |
4 | nfr 1411 | . . 3 | |
5 | stdpc4 1658 | . . 3 | |
6 | 4, 5 | syl6 29 | . 2 |
7 | 3, 6 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wnf 1349 wex 1381 wsb 1645 |
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-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbctt 2824 |
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