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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 𝑥𝜑
eximd.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
eximd (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem eximd
StepHypRef Expression
1 eximd.1 . . 3 𝑥𝜑
21nf5ri 2053 . 2 (𝜑 → ∀𝑥𝜑)
3 eximd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3eximdh 1778 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
 Colors of variables: wff setvar class 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
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