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Theorem sb56 1807
 Description: Two equivalent ways of expressing the proper substitution of for in , when and are distinct. Theorem 6.2 of [Quine] p. 40. The proof does not involve df-sb 1687. (Contributed by NM, 14-Apr-2008.)
Assertion
Ref Expression
sb56
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb56
StepHypRef Expression
1 hba1 1474 . 2
2 ax11v 1749 . . 3
3 ax-4 1441 . . . 4
43com12 30 . . 3
52, 4impbid 127 . 2
61, 5equsex 1657 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wex 1422 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-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  sb6  1808  sb5  1809  alexeq  2722
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