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Theorem oprabbid 6350
Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 24-Jun-2014.)
Hypotheses
Ref Expression
oprabbid.1
oprabbid.2
oprabbid.3
oprabbid.4
Assertion
Ref Expression
oprabbid
Distinct variable groups:   ,   ,

Proof of Theorem oprabbid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 oprabbid.1 . . . 4
2 oprabbid.2 . . . . 5
3 oprabbid.3 . . . . . 6
4 oprabbid.4 . . . . . . 7
54anbi2d 703 . . . . . 6
63, 5exbid 1886 . . . . 5
72, 6exbid 1886 . . . 4
81, 7exbid 1886 . . 3
98abbidv 2593 . 2
10 df-oprab 6300 . 2
11 df-oprab 6300 . 2
129, 10, 113eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  {cab 2442  <.cop 4035  {coprab 6297
This theorem is referenced by:  oprabbidv  6351  mpt2eq123  6356
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  df-oprab 6300
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