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Theorem r19.21be 3204
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 3203 . . 3 ((𝜑𝑥𝐴) → 𝜓)
32expcom 417 . 2 (𝑥𝐴 → (𝜑𝜓))
43rgen 3143 1 𝑥𝐴 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2115  wral 3133
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-ral 3138
This theorem is referenced by:  bnj580  32242
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