Theorem eximd 2224

Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1836. (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 2203	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		eximd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	eximdh 1866	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1781  Ⅎwnf 1785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-ex 1782  df-nf 1786

This theorem is referenced by:  exlimd  2226  19.41  2243  2ax6elem  2475  2euexv  2632  mopick2  2638  2euex  2642  reximd2a  3248  spc2ed  3557  ssrexf  4002  rexdifi  4104  axprlem4OLD  5376  axprlem5OLD  5377  axpowndlem3  10522  axregndlem1  10525  axregnd  10527  padct  32808  dvelimexcased  35253  finminlem  36534  difunieq  37629  wl-euequf  37829  pmapglb2xN  40148  unitscyglem5  42569  infrpge  45710  fsumiunss  45935  islpcn  45997  stoweidlem34  46392  stoweidlem35  46393  sge0rpcpnf  46779