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Theorem r19.21bi 2712
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
r19.21bi.1 (φx A ψ)
Assertion
Ref Expression
r19.21bi ((φ x A) → ψ)

Proof of Theorem r19.21bi
StepHypRef Expression
1 r19.21bi.1 . . . 4 (φx A ψ)
2 df-ral 2619 . . . 4 (x A ψx(x Aψ))
31, 2sylib 188 . . 3 (φx(x Aψ))
4319.21bi 1758 . 2 (φ → (x Aψ))
54imp 418 1 ((φ x A) → ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540   ∈ 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-an 360  df-ex 1542  df-ral 2619 This theorem is referenced by:  rspec2  2713  rspec3  2714  r19.21be  2715  phidisjnn  4615
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