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Theorem alexeq 2897
 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 2292 . . . . 5
32anbi1d 685 . . . 4
43exbidv 1612 . . 3
52imbi1d 308 . . . 4
65albidv 1611 . . 3
7 sb56 2037 . . 3
81, 4, 6, 7vtoclb 2841 . 2
98bicomi 193 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528   wceq 1623   wcel 1684  cvv 2788 This theorem is referenced by:  ceqex  2898  fates  24955  alexeqd  24962 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  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-v 2790
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