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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 2159 with the class variables in wcel 2158. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
cleljust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1536 |
. . 3
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2 | elequ1 2162 |
. . 3
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3 | 1, 2 | equsex 1738 |
. 2
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4 | 3 | bicomi 132 |
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 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-13 2160 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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