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Theorem abeq1 2582
 Description: Equality of a class variable and a class abstraction. (Contributed by NM, 20-Aug-1993.)
Assertion
Ref Expression
abeq1
Distinct variable group:   ,

Proof of Theorem abeq1
StepHypRef Expression
1 abeq2 2581 . 2
2 eqcom 2466 . 2
3 bicom 200 . . 3
43albii 1640 . 2
51, 2, 43bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442 This theorem is referenced by:  abbi1dvOLD  2596  disj  3867  euabsn2  4101  dm0rn0  5224  dffo3  6046  dfsup2  7922  dfsup2OLD  7923  rankf  8233  dfon3  29542  dfiota3  29573 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452
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