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Theorem oprabbid 5563
 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 684 . . . . . 6
63, 5exbid 1773 . . . . 5
72, 6exbid 1773 . . . 4
81, 7exbid 1773 . . 3
98abbidv 2467 . 2
10 df-oprab 5528 . 2
11 df-oprab 5528 . 2
129, 10, 113eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541  wnf 1544   wceq 1642  cab 2339  cop 4561  coprab 5527 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-oprab 5528 This theorem is referenced by:  oprabbidv  5564  mpt2eq123  5661
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