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Mirrors > Home > MPE Home > Th. List > sbt | Structured version Visualization version Unicode version |
Description: A substitution into a theorem yields a theorem. (See chvar 2262 and chvarv 2263 for versions using implicit substitution.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 20-Jul-2018.) |
Ref | Expression |
---|---|
sbt.1 |
Ref | Expression |
---|---|
sbt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc4 2353 | . 2 | |
2 | sbt.1 | . 2 | |
3 | 1, 2 | mpg 1724 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-sb 1881 |
This theorem is referenced by: vjust 3201 iscatd2 16342 iuninc 29379 suppss2f 29439 esumpfinvalf 30138 sbtT 38783 2sb5ndVD 39146 2sb5ndALT 39168 |
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