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Theorem eximd 2069
Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1749. (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 2050 . 2 (𝜑 → ∀𝑥𝜑)
3 eximd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3eximdh 1776 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-12 2031
This theorem depends on definitions:  df-bi 195  df-ex 1695  df-nf 1700
This theorem is referenced by:  exlimd  2071  19.41  2087  19.42-1  2088  2ax6elem  2432  mopick2  2523  2euex  2527  reximd2a  2991  ssrexf  3623  axpowndlem3  9273  axregndlem1  9276  axregnd  9278  spc2ed  28498  padct  28687  finminlem  31284  bj-mo3OLD  31831  wl-euequ1f  32334  pmapglb2xN  33875  disjinfi  38174  infrpge  38308  fsumiunss  38442  islpcn  38506  stoweidlem27  38720  stoweidlem34  38727  stoweidlem35  38728  sge0rpcpnf  39114
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