Theorem bj-exlimh 32602

Description: Closed form of close to exlimih 2148. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-exlimh	⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒)))

Proof of Theorem bj-exlimh

Step	Hyp	Ref	Expression
1		exim 1761	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))
2	1	imim1d 82	1 ⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒)))

Syntax hints:   → wi 4  ∀wal 1481  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bj-exlimh2  32603