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Theorem ceqex 2969
 Description: Equality implies equivalence with substitution. (Contributed by NM, 2-Mar-1995.)
Assertion
Ref Expression
ceqex
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem ceqex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 19.8a 1756 . . 3
2 isset 2863 . . 3
31, 2sylibr 203 . 2
4 eqeq2 2362 . . . 4
54anbi1d 685 . . . . . 6
65exbidv 1626 . . . . 5
76bibi2d 309 . . . 4
84, 7imbi12d 311 . . 3
9 19.8a 1756 . . . . 5
109ex 423 . . . 4
11 vex 2862 . . . . . 6
1211alexeq 2968 . . . . 5
13 sp 1747 . . . . . 6
1413com12 27 . . . . 5
1512, 14syl5bir 209 . . . 4
1610, 15impbid 183 . . 3
178, 16vtoclg 2914 . 2
183, 17mpcom 32 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  ceqsexg  2970  sbc6g  3071
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