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  2839  rexex  3094  imassrn  6071  fv3  6900  elirrvOLD  9573  finacn  10056  dfac4  10128  kmlem2  10157  ac6c5  10487  ac6s3  10492  ac6s5  10496  axnulALT3  35618  bj-finsumval0  38039  mptsnunlem  38094  topdifinffinlem  38103  heiborlem3  38565  ac6s3f  38921  moantr  39122