Theorem exsimpr 1877

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 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1842	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 399  ∃wex 1787

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788

This theorem is referenced by:  19.40  1894  rexex  3152  ceqsexv2d  3447  imassrn  5925  fv3  6713  finacn  9629  dfac4  9701  kmlem2  9730  ac6c5  10061  ac6s3  10066  ac6s5  10070  bj-finsumval0  35140  mptsnunlem  35195  topdifinffinlem  35204  heiborlem3  35657  ac6s3f  36015  moantr  36180