Theorem exsimpr 1864

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 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1829	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774

This theorem is referenced by:  19.40  1881  elex2  2806  rexex  3070  ceqsexv2d  3523  imassrn  6063  fv3  6902  finacn  10044  dfac4  10116  kmlem2  10145  ac6c5  10476  ac6s3  10481  ac6s5  10485  bj-finsumval0  36673  mptsnunlem  36726  topdifinffinlem  36735  heiborlem3  37192  ac6s3f  37550  moantr  37744