Theorem euorv 1025

Description: Introduction of a disjunct into uniqueness quantifier.

Assertion

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

Distinct variable group(s):   φ,x

Proof of Theorem euorv

Step	Hyp	Ref	Expression
1		biorf 551	. . 3 ⊢ (¬ φ → (ψ ↔ (φ ∨ ψ)))
2	1	bieudv 1013	. 2 ⊢ (¬ φ → (∃!xψ ↔ ∃!x(φ ∨ ψ)))
3	2	biimpa 324	1 ⊢ ((¬ φ ∧ ∃!xψ) → ∃!x(φ ∨ ψ))

Syntax hints:  ¬ wn 1   → wi 2   ∨ wo 195   ∧ wa 196  ∃!weu 1007

This theorem is referenced by:  eueq2 1429  eueq3 1430

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-eu 1009

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