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Theorem equveliv 29737
Description: Similar to equveli 1941 without using ax12o 1887. (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 1606 . 2  |-  ( x  =  y  ->  A. z  x  =  y )
2 equequ1 1667 . 2  |-  ( z  =  x  ->  (
z  =  y  <->  x  =  y ) )
31, 2equsalhw 1742 1  |-  ( A. z ( z  =  x  ->  z  =  y )  <->  x  =  y )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530
This theorem is referenced by:  equvelv  29738
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177
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