Theorem exsimpr 1866

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 487	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1831	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 398  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777

This theorem is referenced by:  19.40  1883  spsbeOLDOLD  2507  spsbeALT  2585  rexex  3240  ceqsexv2d  3542  imassrn  5939  fv3  6687  finacn  9475  dfac4  9547  kmlem2  9576  ac6c5  9903  ac6s3  9908  ac6s5  9912  bj-finsumval0  34566  mptsnunlem  34618  topdifinffinlem  34627  heiborlem3  35090  ac6s3f  35448  moantr  35615