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Theorem dfsb7a 1913
Description: An alternate definition of proper substitution df-sb 1688. Similar to dfsb7 1910 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 1912. (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 1462 . 2  |-  F/ z
ph
21sb7af 1912 1  |-  ( [ y  /  x ] ph 
<-> 
A. z ( z  =  y  ->  A. x
( x  =  z  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688
This theorem is referenced by: (None)
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