Theorem bj-exlimmpi 13805

Description: Lemma for bj-vtoclgf 13811. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

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

Proof of Theorem bj-exlimmpi

Step	Hyp	Ref	Expression
1		bj-exlimmp.nf	. 2 ⊢ Ⅎ𝑥𝜓
2		bj-exlimmp.min	. . 3 ⊢ (𝜒 → 𝜑)
3		bj-exlimmpi.maj	. . 3 ⊢ (𝜒 → (𝜑 → 𝜓))
4	2, 3	mpd 13	. 2 ⊢ (𝜒 → 𝜓)
5	1, 4	exlimi 1587	1 ⊢ (∃𝑥𝜒 → 𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1453  ∃wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1442  ax-ie2 1487  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by: (None)