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Theorem r19.2m 3337
 Description: Theorem 19.2 of [Margaris] p. 89 with restricted quantifiers (compare 19.2 1545). The restricted version is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 5-Aug-2018.)
Assertion
Ref Expression
r19.2m
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem r19.2m
StepHypRef Expression
1 df-ral 2328 . . . 4
2 exintr 1541 . . . 4
31, 2sylbi 118 . . 3
4 df-rex 2329 . . 3
53, 4syl6ibr 155 . 2
65impcom 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101  wal 1257  wex 1397   wcel 1409  wral 2323  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443 This theorem depends on definitions:  df-bi 114  df-ral 2328  df-rex 2329 This theorem is referenced by:  intssunim  3665  riinm  3757  trintssmOLD  3899  iinexgm  3936  xpiindim  4501  cnviinm  4887  eusvobj2  5526  iinerm  6209  rexfiuz  9816  r19.2uz  9820  climuni  10045
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