Theorem 2eximdv 1803

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)

Hypothesis

Ref	Expression
2alimdv.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
2eximdv	⊢ (𝜑 → (∃𝑥∃𝑦𝜓 → ∃𝑥∃𝑦𝜒))

Distinct variable groups:   𝜑,𝑥   𝜑,𝑦

Allowed substitution hints:   𝜓(𝑥,𝑦)   𝜒(𝑥,𝑦)

Proof of Theorem 2eximdv

Step	Hyp	Ref	Expression
1		2alimdv.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	eximdv 1801	. 2 ⊢ (𝜑 → (∃𝑦𝜓 → ∃𝑦𝜒))
3	2	eximdv 1801	1 ⊢ (𝜑 → (∃𝑥∃𝑦𝜓 → ∃𝑥∃𝑦𝜒))

Syntax hints:   → wi 4  ∃wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  cgsex2g  2635  cgsex4g  2636  spc2egv  2687  spc3egv  2689  relop  4504  elres  4664  opabbrex  5569  th3q  6234  addnnnq0  6639  mulnnnq0  6640  prmuloc  6756  addsrpr  6922  mulsrpr  6923