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Theorem exsimpl 1860
Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
exsimpl (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)

Proof of Theorem exsimpl
StepHypRef Expression
1 simpl 483 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1826 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by:  19.40  1878  moexexlem  2704  elisset  3503  elex  3510  sbc5  3797  r19.2zb  4437  dmcoss  5835  suppimacnvss  7829  unblem2  8759  kmlem8  9571  isssc  17078  bnj1143  31961  bnj1371  32198  bnj1374  32200  bj-elissetv  34088  atex  36422  rtrclex  39855  clcnvlem  39861  pm10.55  40578
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