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Theorem abeq2f 23965
 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 2567 . . 3
3 hbab1 2427 . . 3
42, 3cleqh 2535 . 2
5 abid 2426 . . . 4
65bibi2i 306 . . 3
76albii 1576 . 2
84, 7bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1550   wceq 1653   wcel 1726  cab 2424  wnfc 2561 This theorem is referenced by:  rabid2f  23972  mptfnf  24078 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563
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