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Theorem sb56 2037
 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 1630. (Contributed by NM, 14-Apr-2008.)
Assertion
Ref Expression
sb56
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb56
StepHypRef Expression
1 nfa1 1756 . 2
2 ax11v 2036 . . 3
3 sp 1716 . . . 4
43com12 27 . . 3
52, 4impbid 183 . 2
61, 5equsex 1902 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528 This theorem is referenced by:  sb6  2038  sb5  2039  alexeq  2897  pm13.196a  27614 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
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