Theorem bj-exlimmpi

Description: Lemma for bj-vtoclg1f1 (an instance of this lemma is a version of bj-vtoclg1f1 where x and y are identified). (Contributed by BJ, 30-Apr-2019) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		bj-exlimmpi.nf	⊢ Ⅎ 𝑥 𝜓
2		bj-exlimmpi.maj	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )
3		bj-exlimmpi.min	⊢ 𝜑
4	3 2	mpi	⊢ ( 𝜒 → 𝜓 )
5	1 4	exlimi	⊢ ( ∃ 𝑥 𝜒 → 𝜓 )