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Mirrors > Home > ILE Home > Th. List > sbt | Unicode version |
Description: A substitution into a theorem remains true. (See chvar 1731 and chvarv 1910 for versions using implicit substitition.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
sbt.1 |
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Ref | Expression |
---|---|
sbt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbt.1 |
. 2
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2 | 1 | nfth 1441 |
. . 3
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3 | 2 | sbf 1751 |
. 2
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4 | 1, 3 | mpbir 145 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
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-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: vjust 2690 |
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