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Theorem ectocld 6108
Description: Implicit substitution of class for equivalence class. (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypotheses
Ref Expression
ectocl.1  S  /. R
ectocl.2  R
ectocld.3
Assertion
Ref Expression
ectocld  S
Distinct variable groups:   ,   ,   , R   ,   ,
Allowed substitution hints:   ()    S()

Proof of Theorem ectocld
StepHypRef Expression
1 elqsi 6094 . . . 4  /. R  R
2 ectocl.1 . . . 4  S  /. R
31, 2eleq2s 2129 . . 3  S  R
4 ectocld.3 . . . . 5
5 ectocl.2 . . . . . 6  R
65eqcoms 2040 . . . . 5  R
74, 6syl5ibcom 144 . . . 4  R
87rexlimdva 2427 . . 3  R
93, 8syl5 28 . 2  S
109imp 115 1  S
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390  wrex 2301  cec 6040   /.cqs 6041
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-qs 6048
This theorem is referenced by:  ectocl  6109  elqsn0m  6110  qsel  6119
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