Theorem exsimpr 1784

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 476	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1752	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 383  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696

This theorem is referenced by:  19.40  1785  spsbe  1871  rexex  2985  ceqsexv2d  3216  imassrn  5396  fv3  6116  finacn  8756  dfac4  8828  kmlem2  8856  ac6c5  9187  ac6s3  9192  ac6s5  9196  bj-finsumval0  32324  mptsnunlem  32361  topdifinffinlem  32371  heiborlem3  32782  ac6s3f  33149