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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 1394 with the class variables in wcel 1393. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
cleljust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1419 |
. . 3
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2 | elequ1 1600 |
. . 3
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3 | 1, 2 | equsex 1616 |
. 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 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-13 1404 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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