Theorem exsimpr 1873

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 1838	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1784

This theorem is referenced by:  19.40  1890  rexex  3167  ceqsexv2d  3471  imassrn  5969  fv3  6774  finacn  9737  dfac4  9809  kmlem2  9838  ac6c5  10169  ac6s3  10174  ac6s5  10178  bj-finsumval0  35383  mptsnunlem  35436  topdifinffinlem  35445  heiborlem3  35898  ac6s3f  36256  moantr  36421