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Mirrors > Home > ILE Home > Th. List > sb8h | Unicode version |
Description: Substitution of variable in universal quantifier. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Jim Kingdon, 15-Jan-2018.) |
Ref | Expression |
---|---|
sb8h.1 |
Ref | Expression |
---|---|
sb8h |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb8h.1 | . 2 | |
2 | 1 | hbsb3 1689 | . 2 |
3 | sbequ12 1654 | . 2 | |
4 | 1, 2, 3 | cbvalh 1636 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbhb 1816 sb8euh 1923 |
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