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Theorem eleq2w 2199
 Description: Weaker version of eleq2 2201 (but more general than elequ2 1691) not depending on ax-ext 2119 nor df-cleq 2130. (Contributed by BJ, 29-Sep-2019.)
Assertion
Ref Expression
eleq2w

Proof of Theorem eleq2w
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elequ2 1691 . . . 4
21anbi2d 459 . . 3
32exbidv 1797 . 2
4 df-clel 2133 . 2
5 df-clel 2133 . 2
63, 4, 53bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wex 1468   wcel 1480 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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-clel 2133 This theorem is referenced by: (None)
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