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Theorem sb56 2098
 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 1649. (Contributed by NM, 14-Apr-2008.)
Assertion
Ref Expression
sb56
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb56
StepHypRef Expression
1 nfa1 1788 . 2
2 ax11v 2096 . . 3
3 sp 1747 . . . 4
43com12 27 . . 3
52, 4impbid 183 . 2
61, 5equsex 1962 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  sb6  2099  sb5  2100  alexeq  2968
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