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  3245  spc2ed  3564  ssrexf  4010  rexdifi  4109  axprlem4OLD  5379  axprlem5OLD  5380  axpowndlem3  10528  axregndlem1  10531  axregnd  10533  padct  32616  dvelimexcased  35040  finminlem  36279  difunieq  37335  wl-euequf  37535  pmapglb2xN  39739  unitscyglem5  42160  infrpge  45320  fsumiunss  45546  islpcn  45610  stoweidlem34  46005  stoweidlem35  46006  sge0rpcpnf  46392