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 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782

This theorem is referenced by:  19.40  1889  elex2  2812  rexex  3076  ceqsexv2d  3528  imassrn  6070  fv3  6909  finacn  10044  dfac4  10116  kmlem2  10145  ac6c5  10476  ac6s3  10481  ac6s5  10485  bj-finsumval0  36161  mptsnunlem  36214  topdifinffinlem  36223  heiborlem3  36676  ac6s3f  37034  moantr  37228