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| 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 2176 with the class variables in wcel 2175. (Contributed by NM, 28-Jan-2004.) |
| Ref | Expression |
|---|---|
| cleljust |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-17 1548 |
. . 3
| |
| 2 | elequ1 2179 |
. . 3
| |
| 3 | 1, 2 | equsex 1750 |
. 2
|
| 4 | 3 | bicomi 132 |
1
|
| 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 1469 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-13 2177 |
| This theorem depends on definitions: df-bi 117 |
| This theorem is referenced by: (None) |
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