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Mirrors > Home > MPE Home > Th. List > sb4 | Structured version Visualization version Unicode version |
Description: One direction of a simplified definition of substitution when variables are distinct. (Contributed by NM, 14-May-1993.) |
Ref | Expression |
---|---|
sb4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb1 1883 | . 2 | |
2 | equs5 2351 | . 2 | |
3 | 1, 2 | syl5ib 234 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wal 1481 wex 1704 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-10 2019 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 |
This theorem is referenced by: sb4b 2358 hbsb2 2359 dfsb2 2373 sbequi 2375 sbi1 2392 |
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