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Theorem ectocl 6931
 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 1327 . 2
2 ectocl.1 . . 3
3 ectocl.2 . . 3
4 ectocl.3 . . . 4
54adantl 453 . . 3
62, 3, 5ectocld 6930 . 2
71, 6mpan 652 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wtru 1322   wceq 1649   wcel 1721  cec 6862  cqs 6863 This theorem is referenced by:  vitalilem2  19454 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-v 2918  df-qs 6870
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