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Theorem rexlimd 2408
Description: Deduction from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Hypotheses
Ref Expression
rexlimd.1 xφ
rexlimd.2 xχ
rexlimd.3 (φ → (x A → (ψχ)))
Assertion
Ref Expression
rexlimd (φ → (x A ψχ))

Proof of Theorem rexlimd
StepHypRef Expression
1 rexlimd.1 . . 3 xφ
2 rexlimd.3 . . 3 (φ → (x A → (ψχ)))
31, 2ralrimi 2368 . 2 (φx A (ψχ))
4 rexlimd.2 . . 3 xχ
54r19.23 2402 . 2 (x A (ψχ) ↔ (x A ψχ))
63, 5sylib 127 1 (φ → (x A ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1329   wcel 1374  wral 2284  wrex 2285
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289  df-rex 2290
This theorem is referenced by:  rexlimdv  2410  ralxfrALT  4149  fvmptt  5187  ffnfv  5248  prarloclem3step  6350  prmuloc2  6411
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