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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 |
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Ref | Expression |
---|---|
sb8h |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb8h.1 |
. 2
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2 | 1 | hbsb3 1819 |
. 2
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3 | sbequ12 1782 |
. 2
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4 | 1, 2, 3 | cbvalh 1764 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: sbhb 1952 sb8euh 2061 |
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