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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 1739 | . 2 | |
2 | equs5 1801 | . 2 | |
3 | 1, 2 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wal 1329 wex 1468 wsb 1735 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 |
This theorem is referenced by: sb4b 1806 hbsb2 1808 |
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