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Theorem equveliv 29115
Description: Similar to equveli 1928 without using ax12o 1875. (Contributed by NM, 7-Nov-1015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equveliv  |-  ( A. z ( z  =  x  ->  z  =  y )  <->  x  =  y )
Distinct variable groups:    x, z    y, z

Proof of Theorem equveliv
StepHypRef Expression
1 ax-17 1603 . 2  |-  ( x  =  y  ->  A. z  x  =  y )
2 equequ1 1648 . 2  |-  ( z  =  x  ->  (
z  =  y  <->  x  =  y ) )
31, 2equsalhw 1730 1  |-  ( A. z ( z  =  x  ->  z  =  y )  <->  x  =  y )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527
This theorem is referenced by:  equvelv  29116
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177
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