Theorem exsimpr 1899

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 489	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1865	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 400  ∃wex 1809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810

This theorem is referenced by:  19.40  1916  elex2  2840  rexex  3095  imassrn  6075  fv3  6901  elirrvOLD  9561  finacn  10035  dfac4  10107  kmlem2  10136  ac6c5  10467  ac6s3  10472  ac6s5  10476  axnulALT3  35483  bj-finsumval0  37910  mptsnunlem  37965  topdifinffinlem  37974  heiborlem3  38445  ac6s3f  38801  moantr  39002