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Theorem abbid 2551
 Description: Equivalent wff's yield equal class abstractions (deduction rule). (Contributed by NM, 5-Aug-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 1782 . 2
4 abbi 2548 . 2
53, 4sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wnf 1554   wceq 1653  cab 2424 This theorem is referenced by:  abbidv  2552  rabeqf  2951  sbcbid  3216  iotain  27596 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431
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