Metamath Proof Explorer

Theorem barbarilem

Description: Lemma for barbari and the other Aristotelian syllogisms with existential assumption. (Contributed by BJ, 16-Sep-2022)

Ref Expression
Hypotheses barbarilem.min x φ
barbarilem.maj x φ ψ
Assertion barbarilem x φ ψ


Step Hyp Ref Expression
1 barbarilem.min x φ
2 barbarilem.maj x φ ψ
3 exintr x φ ψ x φ x φ ψ
4 2 1 3 mp2 x φ ψ