Theorem bj-exlimvmpi

Description: A Fol lemma ( exlimiv followed by mpi ). (Contributed by BJ, 2-Jul-2022) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-exlimvmpi.maj	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )
	bj-exlimvmpi.min	⊢ 𝜑
Assertion	bj-exlimvmpi	⊢ ( ∃ 𝑥 𝜒 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-exlimvmpi.maj	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )
2		bj-exlimvmpi.min	⊢ 𝜑
3	2 1	mpi	⊢ ( 𝜒 → 𝜓 )
4	3	exlimiv	⊢ ( ∃ 𝑥 𝜒 → 𝜓 )