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Theorem alexeq 3067
 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 2447 . . . . 5
32anbi1d 687 . . . 4
43exbidv 1637 . . 3
52imbi1d 310 . . . 4
65albidv 1636 . . 3
7 sb56 2176 . . 3
81, 4, 6, 7vtoclb 3011 . 2
98bicomi 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1726  cvv 2958 This theorem is referenced by:  ceqex  3068 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-v 2960
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