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Theorem sb6 1766
 Description: Equivalence for substitution. Compare Theorem 6.2 of [Quine] p. 40. Also proved as Lemmas 16 and 17 of [Tarski] p. 70. (Contributed by NM, 18-Aug-1993.) (Revised by NM, 14-Apr-2008.)
Assertion
Ref Expression
sb6
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb6
StepHypRef Expression
1 sb56 1765 . . 3
21anbi2i 430 . 2
3 df-sb 1646 . 2
4 ax-4 1400 . . 3
54pm4.71ri 372 . 2
62, 3, 53bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wex 1381  wsb 1645 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-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-sb 1646 This theorem is referenced by:  sb5  1767  sbnv  1768  sbanv  1769  sbi1v  1771  sbi2v  1772  hbs1  1814  2sb6  1860  sbcom2v  1861  sb6a  1864  sb7af  1869  sbalyz  1875  sbal1yz  1877  exsb  1884  sbal2  1898
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