Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  oprabbii Structured version   Unicode version

Theorem oprabbii 6121
 Description: Equivalent wff's yield equal operation class abstractions. (Contributed by NM, 28-May-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Hypothesis
Ref Expression
oprabbii.1
Assertion
Ref Expression
oprabbii
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem oprabbii
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqid 2435 . 2
2 oprabbii.1 . . . 4
32a1i 11 . . 3
43oprabbidv 6120 . 2
51, 4ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652  coprab 6074 This theorem is referenced by:  oprab4  6135  mpt2v  6155  dfxp3  6398  tposmpt2  6508  ovec  7006  addcnsr  9000  mulcnsr  9001 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
 Copyright terms: Public domain W3C validator