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Theorem oprabbidv 6346
 Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.)
Hypothesis
Ref Expression
oprabbidv.1
Assertion
Ref Expression
oprabbidv
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem oprabbidv
StepHypRef Expression
1 nfv 1683 . 2
2 nfv 1683 . 2
3 nfv 1683 . 2
4 oprabbidv.1 . 2
51, 2, 3, 4oprabbid 6345 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1379  coprab 6296 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-oprab 6299 This theorem is referenced by:  oprabbii  6347  mpt2eq123dva  6353  mpt2eq3dva  6356  resoprab2  6394  erovlem  7419  joinfval  15505  meetfval  15519  odumeet  15644  odujoin  15646  mppsval  28757
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