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Theorem sb6 2038
 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.)
Assertion
Ref Expression
sb6
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb6
StepHypRef Expression
1 sb56 2037 . . 3
21anbi2i 675 . 2
3 df-sb 1630 . 2
4 sp 1716 . . 3
54pm4.71ri 614 . 2
62, 3, 53bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528  wsb 1629 This theorem is referenced by:  sb5  2039  2sb6  2052  sb6a  2055  exsbOLD  2070  sbal2  2073 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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