Theorem bj-2exim 34720

Description: Closed form of 2eximi 1839. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-2exim	⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓))

Proof of Theorem bj-2exim

Step	Hyp	Ref	Expression
1		exim 1837	. 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∃𝑦𝜑 → ∃𝑦𝜓))
2	1	aleximi 1835	1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by: (None)