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Theorem ectocld 5991
 Description: Implicit substitution of class for equivalence class. (Contributed by set.mm contributors, 9-Jul-2014.)
Hypotheses
Ref Expression
ectocl.1
ectocl.2
ectocld.3
Assertion
Ref Expression
ectocld
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ectocld
StepHypRef Expression
1 elqsi 5978 . . . 4
2 ectocl.1 . . . 4
31, 2eleq2s 2445 . . 3
4 ectocld.3 . . . . 5
5 ectocl.2 . . . . . 6
65eqcoms 2356 . . . . 5
74, 6syl5ibcom 211 . . . 4
87rexlimdva 2738 . . 3
93, 8syl5 28 . 2
109imp 418 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  wrex 2615  cec 5945  cqs 5946 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-ral 2619  df-rex 2620  df-v 2861  df-qs 5951 This theorem is referenced by:  ectocl  5992  elqsn0  5993  qsdisj  5995
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