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Theorem eximd 2083
Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1759. (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 2063 . 2 (𝜑 → ∀𝑥𝜑)
3 eximd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3eximdh 1789 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1702  wnf 1706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-ex 1703  df-nf 1708
This theorem is referenced by:  exlimd  2085  19.41  2101  19.42-1  2102  2ax6elem  2447  mopick2  2538  2euex  2542  reximd2a  3010  ssrexf  3657  axpowndlem3  9406  axregndlem1  9409  axregnd  9411  spc2ed  29282  padct  29471  finminlem  32287  bj-mo3OLD  32807  wl-euequ1f  33327  pmapglb2xN  34877  disjinfi  39196  infrpge  39380  fsumiunss  39607  islpcn  39671  stoweidlem27  40007  stoweidlem34  40014  stoweidlem35  40015  sge0rpcpnf  40401
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