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Theorem rmoeq1 2502
Description: Equality theorem for restricted uniqueness quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
rmoeq1 (A = B → (∃*x A φ∃*x B φ))
Distinct variable groups:   x,A   x,B
Allowed substitution hint:   φ(x)

Proof of Theorem rmoeq1
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfcv 2175 . 2 xB
31, 2rmoeq1f 2498 1 (A = B → (∃*x A φ∃*x B φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242  ∃*wrmo 2303
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-eu 1900  df-mo 1901  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rmo 2308
This theorem is referenced by:  rmoeqd  2510
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