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Mirrors > Home > ILE Home > Th. List > cleljust | Unicode version |
Description: When the class variables of set theory are replaced with setvar variables, this theorem of predicate calculus is the result. This theorem provides part of the justification for the consistency of that definition, which "overloads" the setvar variables in wel 1391 with the class variables in wcel 1390. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
cleljust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1416 |
. . 3
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2 | elequ1 1597 |
. . 3
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3 | 1, 2 | equsex 1613 |
. 2
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4 | 3 | bicomi 123 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-13 1401 ax-17 1416 ax-i9 1420 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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