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Theorem ralrimi 2384
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 1412 . 2 (φx(x Aψ))
4 df-ral 2305 . 2 (x A ψx(x Aψ))
53, 4sylibr 137 1 (φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346   wcel 1390  wral 2300
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-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  ralrimiv  2385  reximdai  2411  r19.12  2416  rexlimd  2424  rexlimd2  2425  r19.29af2  2446  r19.37  2456  ralidm  3315  iineq2d  3668  mpteq2da  3837  mpteqb  5204  eusvobj2  5441  tfri3  5894
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