Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  rspceeqv Unicode version

Theorem rspceeqv 2813
 Description: Restricted existential specialization in an equality, using implicit substitution. (Contributed by BJ, 2-Sep-2022.)
Hypothesis
Ref Expression
rspceeqv.1
Assertion
Ref Expression
rspceeqv
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rspceeqv
StepHypRef Expression
1 rspceeqv.1 . . 3
21eqeq2d 2153 . 2
32rspcev 2795 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   wcel 2112  wrex 2419 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-rex 2424  df-v 2693 This theorem is referenced by:  elixpsn  6641  ixpsnf1o  6642  elfir  6878  0ct  7009  ctmlemr  7010  ctssdclemn0  7012  fodju0  7040  mertenslemi1  11365  mertenslem2  11366  ctiunctlemfo  12024  elrestr  12203  restopnb  12425  mopnex  12749  metrest  12750
 Copyright terms: Public domain W3C validator