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Theorem ectocl 6975
 Description: Implicit substitution of class for equivalence class. (Contributed by NM, 23-Jul-1995.) (Revised by Mario Carneiro, 9-Jul-2014.)
Hypotheses
Ref Expression
ectocl.1
ectocl.2
ectocl.3
Assertion
Ref Expression
ectocl
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ectocl
StepHypRef Expression
1 tru 1331 . 2
2 ectocl.1 . . 3
3 ectocl.2 . . 3
4 ectocl.3 . . . 4
54adantl 454 . . 3
62, 3, 5ectocld 6974 . 2
71, 6mpan 653 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wtru 1326   wceq 1653   wcel 1726  cec 6906  cqs 6907 This theorem is referenced by:  vitalilem2  19506 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-qs 6914
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