Theorem euorv 2232

Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 23-Mar-1995.)

Assertion

Ref	Expression
euorv	⊢ ((¬ φ ∧ ∃!xψ) → ∃!x(φ ∨ ψ))

Distinct variable group:   φ,x

Allowed substitution hint:   ψ(x)

Proof of Theorem euorv

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2	1	euor 2231	1 ⊢ ((¬ φ ∧ ∃!xψ) → ∃!x(φ ∨ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∧ wa 358  ∃!weu 2204

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208

This theorem is referenced by:  eueq2  3011