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Theorem ceqex 3230
Description: Equality implies equivalence with substitution. (Contributed by NM, 2-Mar-1995.) (Proof shortened by BJ, 1-May-2019.)
Assertion
Ref Expression
ceqex
Distinct variable group:   ,

Proof of Theorem ceqex
StepHypRef Expression
1 19.8a 1857 . . 3
21ex 434 . 2
3 eqvisset 3117 . . . 4
4 alexeqg 3228 . . . 4
53, 4syl 16 . . 3
6 sp 1859 . . . 4
76com12 31 . . 3
85, 7sylbird 235 . 2
92, 8impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109
This theorem is referenced by:  ceqsexg  3231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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