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Mirrors > Home > ILE Home > Th. List > sbt | Unicode version |
Description: A substitution into a theorem remains true. (See chvar 1640 and chvarv 1812 for versions using implicit substitition.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
sbt.1 |
Ref | Expression |
---|---|
sbt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbt.1 | . 2 | |
2 | 1 | nfth 1353 | . . 3 |
3 | 2 | sbf 1660 | . 2 |
4 | 1, 3 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: vjust 2558 |
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