Theorem eximd 1612

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

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

Assertion

Ref	Expression
eximd	⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem eximd

Step	Hyp	Ref	Expression
1		eximd.1	. . 3 ⊢ Ⅎ𝑥𝜑
2	1	nfri 1519	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		eximd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	eximdh 1611	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  Ⅎwnf 1460  ∃wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461

This theorem is referenced by:  19.41  1686  mo2icl  2916  ssrexf  3217  copsexg  4243  ssopab2  4274  eunex  4559  spc2ed  6231