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Theorem exa1 1754
Description: Add an antecedent in an existentially quantified formula. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
exa1 (∃𝑥𝜑 → ∃𝑥(𝜓𝜑))

Proof of Theorem exa1
StepHypRef Expression
1 ax-1 6 . 2 (𝜑 → (𝜓𝜑))
21eximi 1750 1 (∃𝑥𝜑 → ∃𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by:  19.35  1792
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