Theorem exlimdvv 1777

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.)

Hypothesis

Ref	Expression
exlimdvv.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
exlimdvv	⊢ (𝜑 → (∃𝑥∃𝑦𝜓 → 𝜒))

Distinct variable groups:   𝜒,𝑥   𝜑,𝑥   𝜒,𝑦   𝜑,𝑦

Allowed substitution hints:   𝜓(𝑥,𝑦)

Proof of Theorem exlimdvv

Step	Hyp	Ref	Expression
1		exlimdvv.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	exlimdv 1700	. 2 ⊢ (𝜑 → (∃𝑦𝜓 → 𝜒))
3	2	exlimdv 1700	1 ⊢ (𝜑 → (∃𝑥∃𝑦𝜓 → 𝜒))

Syntax hints:   → wi 4  ∃wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-17 1419

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  euotd  3991  funopg  4934  th3qlem1  6208  fundmen  6286  addnq0mo  6545  mulnq0mo  6546  genprndl  6619  genprndu  6620  genpdisj  6621  mullocpr  6669  addsrmo  6828  mulsrmo  6829