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Theorem ralrimi 2368
Description: Inference from Theorem 19.21 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 10-Oct-1999.)
Hypotheses
Ref Expression
ralrimi.1 xφ
ralrimi.2 (φ → (x Aψ))
Assertion
Ref Expression
ralrimi (φx A ψ)

Proof of Theorem ralrimi
StepHypRef Expression
1 ralrimi.1 . . 3 xφ
2 ralrimi.2 . . 3 (φ → (x Aψ))
31, 2alrimi 1396 . 2 (φx(x Aψ))
4 df-ral 2289 . 2 (x A ψx(x Aψ))
53, 4sylibr 137 1 (φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1226  wnf 1329   wcel 1374  wral 2284
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-4 1381
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289
This theorem is referenced by:  ralrimiv  2369  reximdai  2395  r19.12  2400  rexlimd  2408  rexlimd2  2409  r19.29af2  2430  r19.37  2440  ralidm  3300  iineq2d  3651  mpteq2da  3820  mpteqb  5186  eusvobj2  5422  tfri3  5875
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