Theorem bj-exlimmpbi 36872

Description: Lemma for theorems of the vtoclg 3566 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-exlimmpbi.nf	⊢ Ⅎ𝑥𝜓
bj-exlimmpbi.maj	⊢ (𝜒 → (𝜑 ↔ 𝜓))
bj-exlimmpbi.min	⊢ 𝜑

Assertion

Ref	Expression
bj-exlimmpbi	⊢ (∃𝑥𝜒 → 𝜓)

Proof of Theorem bj-exlimmpbi

Step	Hyp	Ref	Expression
1		bj-exlimmpbi.nf	. 2 ⊢ Ⅎ𝑥𝜓
2		bj-exlimmpbi.min	. . 3 ⊢ 𝜑
3		bj-exlimmpbi.maj	. . 3 ⊢ (𝜒 → (𝜑 ↔ 𝜓))
4	2, 3	mpbii 233	. 2 ⊢ (𝜒 → 𝜓)
5	1, 4	exlimi 2218	1 ⊢ (∃𝑥𝜒 → 𝜓)

Syntax hints:   → wi 4   ↔ wb 206  ∃wex 1777  Ⅎwnf 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-ex 1778  df-nf 1782

This theorem is referenced by: (None)