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Theorem rexlimi 2420
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 30-Nov-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Hypotheses
Ref Expression
rexlimi.1 xψ
rexlimi.2 (x A → (φψ))
Assertion
Ref Expression
rexlimi (x A φψ)

Proof of Theorem rexlimi
StepHypRef Expression
1 rexlimi.2 . . 3 (x A → (φψ))
21rgen 2368 . 2 x A (φψ)
3 rexlimi.1 . . 3 xψ
43r19.23 2418 . 2 (x A (φψ) ↔ (x A φψ))
52, 4mpbi 133 1 (x A φψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1346   wcel 1390  wral 2300  wrex 2301
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306
This theorem is referenced by:  rexlimiv  2421  r19.29af2  2446  triun  3858  reusv1  4156  reusv3  4158  fun11iun  5090
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