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Theorem abeq2f 23913
 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 2533 . . 3
3 hbab1 2393 . . 3
42, 3cleqh 2501 . 2
5 abid 2392 . . . 4
65bibi2i 305 . . 3
76albii 1572 . 2
84, 7bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1546   wceq 1649   wcel 1721  cab 2390  wnfc 2527 This theorem is referenced by:  rabid2f  23920  mptfnf  24026 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529
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