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Mirrors > Home > MPE Home > Th. List > sb1 | Structured version Visualization version Unicode version |
Description: One direction of a simplified definition of substitution. The converse requires either a dv condition (sb5 2430) or a non-freeness hypothesis (sb5f 2386). (Contributed by NM, 13-May-1993.) |
Ref | Expression |
---|---|
sb1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sb 1881 | . 2 | |
2 | 1 | simprbi 480 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wex 1704 wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 df-sb 1881 |
This theorem is referenced by: spsbe 1884 sb4 2356 sb4a 2357 sb4e 2362 sb6 2429 bj-sb4v 32757 bj-sb6 32767 bj-sb3b 32804 wl-sb5nae 33340 |
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