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Theorem abbid 2592
Description: Equivalent wff's yield equal class abstractions (deduction rule). (Contributed by NM, 21-Jun-1993.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
abbid.1
abbid.2
Assertion
Ref Expression
abbid

Proof of Theorem abbid
StepHypRef Expression
1 abbid.1 . . 3
2 abbid.2 . . 3
31, 2alrimi 1877 . 2
4 abbi 2588 . 2
53, 4sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  {cab 2442
This theorem is referenced by:  abbidv  2593  rabeqf  3102  sbcbid  3385  sbceqbidf  27380  opabdm  27464  opabrn  27465  fpwrelmap  27556  iotain  31324  bj-rabbida2  34485
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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