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Theorem oprabbid 6119
 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 685 . . . . . 6
63, 5exbid 1789 . . . . 5
72, 6exbid 1789 . . . 4
81, 7exbid 1789 . . 3
98abbidv 2549 . 2
10 df-oprab 6077 . 2
11 df-oprab 6077 . 2
129, 10, 113eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652  cab 2421  cop 3809  coprab 6074 This theorem is referenced by:  oprabbidv  6120  mpt2eq123  6125 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-oprab 6077
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