Theorem exsimpr 1876

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 1842	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 396  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787

This theorem is referenced by:  19.40  1893  elex2  2817  rexex  3070  ceqsexv2dOLD  3483  imassrn  6030  fv3  6852  elirrvOLD  9510  finacn  9970  dfac4  10042  kmlem2  10072  ac6c5  10402  ac6s3  10407  ac6s5  10411  axnulALT3  35296  bj-finsumval0  37652  mptsnunlem  37707  topdifinffinlem  37716  heiborlem3  38187  ac6s3f  38545  moantr  38746