Theorem exsimpr 1902

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
exsimpr	⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Proof of Theorem exsimpr

Step	Hyp	Ref	Expression
1		simpr 490	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1868	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813

This theorem is used by:  19.40  1919  elex2  2837  rexex  3092  imassrn  6067  fv3  6896  elirrvOLD  9570  finacn  10053  dfac4  10125  kmlem2  10154  ac6c5  10484  ac6s3  10489  ac6s5  10493  axnulALT3  35616  bj-finsumval0  38037  mptsnunlem  38092  topdifinffinlem  38101  heiborlem3  38563  ac6s3f  38919  moantr  39120