New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  oprabbidv Unicode version

Theorem oprabbidv 5564
 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 1619 . 2
2 nfv 1619 . 2
3 nfv 1619 . 2
4 oprabbidv.1 . 2
51, 2, 3, 4oprabbid 5563 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642  coprab 5527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  oprabbii  5565  resoprab2  5582  mpt2eq123dv  5663  mpt2eq3dva  5669
 Copyright terms: Public domain W3C validator