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Theorem alexeq 2814
 Description: Two ways to express substitution of for in . (Contributed by NM, 2-Mar-1995.)
Hypothesis
Ref Expression
alexeq.1
Assertion
Ref Expression
alexeq
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem alexeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 alexeq.1 . . 3
2 eqeq2 2150 . . . . 5
32anbi1d 461 . . . 4
43exbidv 1798 . . 3
52imbi1d 230 . . . 4
65albidv 1797 . . 3
7 sb56 1858 . . 3
81, 4, 6, 7vtoclb 2746 . 2
98bicomi 131 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1330   wceq 1332  wex 1469   wcel 1481  cvv 2689 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-v 2691 This theorem is referenced by:  ceqex  2815
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