Theorem bj-exlimmpbir

Description: Lemma for theorems of the vtoclg family. (Contributed by BJ, 3-Oct-2019) (Proof modification is discouraged.)

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

Proof

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