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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 2136 with the class variables in wcel 2135. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
cleljust |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1513 | . . 3 | |
2 | elequ1 2139 | . . 3 | |
3 | 1, 2 | equsex 1715 | . 2 |
4 | 3 | bicomi 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1479 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-13 2137 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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