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Theorem barbarilem 2752
Description: Lemma for barbari 2753 and the other Aristotelian syllogisms with existential assumption. (Contributed by BJ, 16-Sep-2022.)
Hypotheses
Ref Expression
barbarilem.min 𝑥𝜑
barbarilem.maj 𝑥(𝜑𝜓)
Assertion
Ref Expression
barbarilem 𝑥(𝜑𝜓)

Proof of Theorem barbarilem
StepHypRef Expression
1 barbarilem.maj . 2 𝑥(𝜑𝜓)
2 barbarilem.min . 2 𝑥𝜑
3 exintr 1893 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
41, 2, 3mp2 9 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wal 1535  wex 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781
This theorem is referenced by:  barbari  2753  cesaro  2762  camestros  2763  calemos  2774
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