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Theorem r19.21be 3135
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994.)
Hypothesis
Ref Expression
r19.21be.1 (𝜑 → ∀𝑥𝐴 𝜓)
Assertion
Ref Expression
r19.21be 𝑥𝐴 (𝜑𝜓)

Proof of Theorem r19.21be
StepHypRef Expression
1 r19.21be.1 . . . 4 (𝜑 → ∀𝑥𝐴 𝜓)
21r19.21bi 3134 . . 3 ((𝜑𝑥𝐴) → 𝜓)
32expcom 414 . 2 (𝑥𝐴 → (𝜑𝜓))
43rgen 3074 1 𝑥𝐴 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  wral 3064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-ral 3069
This theorem is referenced by:  bnj580  32893
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