Theorem bj-exlimmpbi

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

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

Proof

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