Theorem exsimpl 1835

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
exsimpl	⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑)

Proof of Theorem exsimpl

Step	Hyp	Ref	Expression
1		simpl 472	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	eximi 1802	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑)

Syntax hints:   → wi 4   ∧ wa 383  ∃wex 1744

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777

This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745

This theorem is referenced by:  19.40  1837  euexALT  2540  moexex  2570  elex  3243  sbc5  3493  r19.2zb  4094  dmcoss  5417  suppimacnvss  7350  unblem2  8254  kmlem8  9017  isssc  16527  bnj1143  30987  bnj1371  31223  bnj1374  31225  bj-elissetv  32986  atex  35010  rtrclex  38241  clcnvlem  38247  pm10.55  38885