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Mirrors > Home > ILE Home > Th. List > sb4 | Unicode version |
Description: One direction of a simplified definition of substitution when variables are distinct. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sb4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb1 1649 | . 2 | |
2 | equs5 1710 | . 2 | |
3 | 1, 2 | syl5 28 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wal 1241 wex 1381 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sb4b 1715 hbsb2 1717 |
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