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Theorem nfeqOLD 2641
Description: Obsolete proof of nfeq 2640 as of 16-Nov-2019. (Contributed by NM, 21-Jun-1993.) (Revised by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
nfnfc.1  |-  F/_ x A
nfeq.2  |-  F/_ x B
Assertion
Ref Expression
nfeqOLD  |-  F/ x  A  =  B

Proof of Theorem nfeqOLD
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2460 . 2  |-  ( A  =  B  <->  A. z
( z  e.  A  <->  z  e.  B ) )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2622 . . . 4  |-  F/ x  z  e.  A
4 nfeq.2 . . . . 5  |-  F/_ x B
54nfcri 2622 . . . 4  |-  F/ x  z  e.  B
63, 5nfbi 1881 . . 3  |-  F/ x
( z  e.  A  <->  z  e.  B )
76nfal 1894 . 2  |-  F/ x A. z ( z  e.  A  <->  z  e.  B
)
81, 7nfxfr 1625 1  |-  F/ x  A  =  B
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   A.wal 1377    = wceq 1379   F/wnf 1599    e. wcel 1767   F/_wnfc 2615
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-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-cleq 2459  df-clel 2462  df-nfc 2617
This theorem is referenced by: (None)
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