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Theorem sb56 1991
 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 1883. (Contributed by NM, 14-Apr-2008.)
Assertion
Ref Expression
sb56
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb56
StepHypRef Expression
1 nfa1 1719 . 2
2 ax11v 1990 . . 3
3 ax-4 1692 . . . 4
43com12 29 . . 3
52, 4impbid 185 . 2
61, 5equsex 1852 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619 This theorem is referenced by:  sb6  1992  sb5  1993  alexeq  2834  pm13.196a  26781 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
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