Theorem exsimpr 1872

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 485	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1837	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 396  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783

This theorem is referenced by:  19.40  1889  elex2  2818  rexex  3171  ceqsexv2d  3481  imassrn  5980  fv3  6792  finacn  9806  dfac4  9878  kmlem2  9907  ac6c5  10238  ac6s3  10243  ac6s5  10247  bj-finsumval0  35456  mptsnunlem  35509  topdifinffinlem  35518  heiborlem3  35971  ac6s3f  36329  moantr  36494