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Theorem sb6 2177
 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 2176 . . 3
21anbi2i 677 . 2
3 df-sb 1660 . 2
4 sp 1764 . . 3
54pm4.71ri 616 . 2
62, 3, 53bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551  wsb 1659 This theorem is referenced by:  sb5  2178  2sb6  2191  sb6a  2195  exsbOLD  2210  sbal2  2213 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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