Theorem exsimpr 1901

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 1867	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812

This theorem is used by:  19.40  1918  elex2  2837  rexex  3092  imassrnOLD  6068  fv3  6904  elirrvOLD  9596  finacn  10133  dfac4  10205  kmlem2  10234  ac6c5  10564  ac6s3  10569  ac6s5  10573  axnulALT3  35786  bj-finsumval0  38300  mptsnunlem  38355  topdifinffinlem  38364  heiborlem3  38841  ac6s3f  39197  moantr  39398