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Theorem abeq2f 23145
 Description: Equality of a class variable and a class abstraction. In this version, the fact that is a non-free variable in is explicitely stated as a hypothesis. (Contributed by Thierry Arnoux, 11-May-2017.)
Hypothesis
Ref Expression
abeq2f.0
Assertion
Ref Expression
abeq2f

Proof of Theorem abeq2f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 abeq2f.0 . . . 4
21nfcrii 2425 . . 3
3 hbab1 2285 . . 3
42, 3cleqh 2393 . 2
5 abid 2284 . . . 4
65bibi2i 304 . . 3
76albii 1556 . 2
84, 7bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176  wal 1530   wceq 1632   wcel 1696  cab 2282  wnfc 2419 This theorem is referenced by:  mptfnf  23241 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421
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