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Theorem rspcedeq2vd 2753
 Description: Restricted existential specialization, using implicit substitution. Variant of rspcedvd 2750 for equations, in which the right hand side depends on the quantified variable. (Contributed by AV, 24-Dec-2019.)
Hypotheses
Ref Expression
rspcedeqvd.1
rspcedeqvd.2
Assertion
Ref Expression
rspcedeq2vd
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rspcedeq2vd
StepHypRef Expression
1 rspcedeqvd.1 . 2
2 rspcedeqvd.2 . . . 4
32eqcomd 2105 . . 3
43eqeq2d 2111 . 2
5 eqidd 2101 . 2
61, 4, 5rspcedvd 2750 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1299   wcel 1448  wrex 2376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082 This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-rex 2381  df-v 2643 This theorem is referenced by: (None)
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