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Theorem oprabbid 6363
 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:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)

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 718 . . . . . 6
63, 5exbid 1984 . . . . 5
72, 6exbid 1984 . . . 4
81, 7exbid 1984 . . 3
98abbidv 2589 . 2
10 df-oprab 6312 . 2
11 df-oprab 6312 . 2
129, 10, 113eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   wceq 1452  wex 1671  wnf 1675  cab 2457  cop 3965  coprab 6309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-oprab 6312 This theorem is referenced by:  oprabbidv  6364  mpt2eq123  6369
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