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Mirrors > Home > MPE Home > Th. List > cleljust | Structured version Visualization version Unicode version |
Description: When the class variables
in definition df-clel 2467 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 1905
with
the class variables in wcel 1904. (Contributed by NM, 28-Jan-2004.)
Revised to use equsexvw 1856 in order to remove dependencies on ax-10 1932,
ax-12 1950, ax-13 2104. Note that there is no DV condition
on ![]() ![]() ![]() |
Ref | Expression |
---|---|
cleljust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ1 1911 |
. . 3
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2 | 1 | equsexvw 1856 |
. 2
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3 | 2 | bicomi 207 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 |
This theorem depends on definitions: df-bi 190 df-an 378 df-ex 1672 |
This theorem is referenced by: bj-dfclel 31565 |
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