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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 1464 with the class variables in wcel 1463. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
cleljust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1489 |
. . 3
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2 | elequ1 1673 |
. . 3
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3 | 1, 2 | equsex 1689 |
. 2
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4 | 3 | bicomi 131 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-4 1470 ax-13 1474 ax-17 1489 ax-i9 1493 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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