Theorem eximd 2085

Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1761. (Contributed by NM, 29-Jun-1993.) (Revised 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	nf5ri 2065	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		eximd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	eximdh 1791	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1704  Ⅎwnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by:  exlimd  2087  19.41  2103  19.42-1  2104  2ax6elem  2449  mopick2  2540  2euex  2544  reximd2a  3013  ssrexf  3665  axpowndlem3  9421  axregndlem1  9424  axregnd  9426  spc2ed  29312  padct  29497  finminlem  32312  bj-mo3OLD  32832  wl-euequ1f  33356  pmapglb2xN  35058  disjinfi  39380  infrpge  39567  fsumiunss  39807  islpcn  39871  stoweidlem27  40244  stoweidlem34  40251  stoweidlem35  40252  sge0rpcpnf  40638