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Theorem alsi1d 42346
 Description: Deduction rule: Given "all some" applied to a top-level inference, you can extract the "for all" part. (Contributed by David A. Wheeler, 20-Oct-2018.)
Hypothesis
Ref Expression
alsi1d.1 (𝜑 → ∀!𝑥(𝜓𝜒))
Assertion
Ref Expression
alsi1d (𝜑 → ∀𝑥(𝜓𝜒))

Proof of Theorem alsi1d
StepHypRef Expression
1 alsi1d.1 . . 3 (𝜑 → ∀!𝑥(𝜓𝜒))
2 df-alsi 42343 . . 3 (∀!𝑥(𝜓𝜒) ↔ (∀𝑥(𝜓𝜒) ∧ ∃𝑥𝜓))
31, 2sylib 207 . 2 (𝜑 → (∀𝑥(𝜓𝜒) ∧ ∃𝑥𝜓))
43simpld 474 1 (𝜑 → ∀𝑥(𝜓𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∀wal 1473  ∃wex 1695  ∀!walsi 42341 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 196  df-an 385  df-alsi 42343 This theorem is referenced by: (None)
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