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  2475  2euexv  2631  mopick2  2637  2euex  2641  reximd2a  3256  spc2ed  3585  ssrexf  4030  rexdifi  4130  axprlem4OLD  5404  axprlem5OLD  5405  axpowndlem3  10618  axregndlem1  10621  axregnd  10623  padct  32702  dvelimexcased  35113  finminlem  36341  difunieq  37397  wl-euequf  37597  pmapglb2xN  39796  unitscyglem5  42217  infrpge  45345  fsumiunss  45571  islpcn  45635  stoweidlem34  46030  stoweidlem35  46031  sge0rpcpnf  46417