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Theorem dfsb7a 1945
Description: An alternate definition of proper substitution df-sb 1719. Similar to dfsb7 1942 in that it involves a dummy variable  z, but expressed in terms of  A. rather than  E.. For a version which only requires  F/ z ph rather than  z and  ph being distinct, see sb7af 1944. (Contributed by Jim Kingdon, 5-Feb-2018.)
Assertion
Ref Expression
dfsb7a  |-  ( [ y  /  x ] ph 
<-> 
A. z ( z  =  y  ->  A. x
( x  =  z  ->  ph ) ) )
Distinct variable groups:    x, z    y,
z    ph, z
Allowed substitution hints:    ph( x, y)

Proof of Theorem dfsb7a
StepHypRef Expression
1 nfv 1491 . 2  |-  F/ z
ph
21sb7af 1944 1  |-  ( [ y  /  x ] ph 
<-> 
A. z ( z  =  y  ->  A. x
( x  =  z  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719
This theorem is referenced by: (None)
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