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Theorem ralrimi 2695
 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 1765 . 2 (φx(x Aψ))
4 df-ral 2619 . 2 (x A ψx(x Aψ))
53, 4sylibr 203 1 (φx A ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  ralrimiv  2696  reximdai  2722  r19.12  2727  rexlimd  2735  rexlimd2  2736  r19.37  2760  ralcom2  2775  2rmorex  3040  iineq2d  3989  ncfinraise  4481  mpteq2da  5666
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