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  3239  spc2ed  3556  ssrexf  4002  rexdifi  4101  axprlem4OLD  5368  axprlem5OLD  5369  axpowndlem3  10493  axregndlem1  10496  axregnd  10498  padct  32662  dvelimexcased  35044  finminlem  36292  difunieq  37348  wl-euequf  37548  pmapglb2xN  39751  unitscyglem5  42172  infrpge  45331  fsumiunss  45556  islpcn  45620  stoweidlem34  46015  stoweidlem35  46016  sge0rpcpnf  46402