Theorem eximd 2072

Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1751. (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 2053	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		eximd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	eximdh 1778	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1695  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701

This theorem is referenced by:  exlimd  2074  19.41  2090  19.42-1  2091  2ax6elem  2437  mopick2  2528  2euex  2532  reximd2a  2996  ssrexf  3628  axpowndlem3  9300  axregndlem1  9303  axregnd  9305  spc2ed  28696  padct  28885  finminlem  31482  bj-mo3OLD  32022  wl-euequ1f  32535  pmapglb2xN  34076  disjinfi  38375  infrpge  38508  fsumiunss  38642  islpcn  38706  stoweidlem27  38920  stoweidlem34  38927  stoweidlem35  38928  sge0rpcpnf  39314