Theorem eximd 2217

Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1834. (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 2196	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		eximd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	eximdh 1864	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1779  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-ex 1780  df-nf 1784

This theorem is referenced by:  exlimd  2219  19.41  2236  2ax6elem  2468  2euexv  2624  mopick2  2630  2euex  2634  reximd2a  3247  spc2ed  3567  ssrexf  4013  rexdifi  4113  axprlem4OLD  5384  axprlem5OLD  5385  axpowndlem3  10552  axregndlem1  10555  axregnd  10557  padct  32643  dvelimexcased  35067  finminlem  36306  difunieq  37362  wl-euequf  37562  pmapglb2xN  39766  unitscyglem5  42187  infrpge  45347  fsumiunss  45573  islpcn  45637  stoweidlem34  46032  stoweidlem35  46033  sge0rpcpnf  46419