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Theorem dfsb7a 1867
 Description: An alternative definition of proper substitution df-sb 1643. Similar to dfsb7 1864 in that it involves a dummy variable z, but expressed in terms of ∀ rather than ∃. For a version which only requires Ⅎzφ rather than z and φ being distinct, see sb7af 1866. (Contributed by Jim Kingdon, 5-Feb-2018.)
Assertion
Ref Expression
dfsb7a ([y / x]φz(z = yx(x = zφ)))
Distinct variable groups:   x,z   y,z   φ,z
Allowed substitution hints:   φ(x,y)

Proof of Theorem dfsb7a
StepHypRef Expression
1 nfv 1418 . 2 zφ
21sb7af 1866 1 ([y / x]φz(z = yx(x = zφ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  [wsb 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643 This theorem is referenced by: (None)
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