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Mirrors > Home > ILE Home > Th. List > sbt | Unicode version |
Description: A substitution into a theorem remains true. (See chvar 1680 and chvarv 1853 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 1393 | . . 3 |
3 | 2 | sbf 1700 | . 2 |
4 | 1, 3 | mpbir 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wsb 1685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 |
This theorem is referenced by: vjust 2602 |
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