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Theorem eqcomOLD 2430
Description: Obsolete proof of eqcom 2429 as of 19-Nov-2019. (Contributed by NM, 26-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
eqcomOLD  |-  ( A  =  B  <->  B  =  A )

Proof of Theorem eqcomOLD
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 bicom 203 . . 3  |-  ( ( x  e.  A  <->  x  e.  B )  <->  ( x  e.  B  <->  x  e.  A
) )
21albii 1687 . 2  |-  ( A. x ( x  e.  A  <->  x  e.  B
)  <->  A. x ( x  e.  B  <->  x  e.  A ) )
3 dfcleq 2413 . 2  |-  ( A  =  B  <->  A. x
( x  e.  A  <->  x  e.  B ) )
4 dfcleq 2413 . 2  |-  ( B  =  A  <->  A. x
( x  e.  B  <->  x  e.  A ) )
52, 3, 43bitr4i 280 1  |-  ( A  =  B  <->  B  =  A )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187   A.wal 1435    = wceq 1437    e. wcel 1867
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-cleq 2412
This theorem is referenced by:  eqcomdOLD  2431
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