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Theorem sb6 1992
 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 1991 . . 3
21anbi2i 678 . 2
3 df-sb 1883 . 2
4 ax-4 1692 . . 3
54pm4.71ri 617 . 2
62, 3, 53bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537  wsb 1882 This theorem is referenced by:  sb5  1993  2sb6  2073  sb6a  2076  exsb  2090  sbal2  2100 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883
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