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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 1780 | . 2 |
3 | sbequ12 1744 | . 2 | |
4 | 1, 2, 3 | cbvalh 1726 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: sbhb 1913 sb8euh 2022 |
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