Metamath Proof Explorer


Theorem eubidv

Description: Formula-building rule for unique existential quantifier (deduction form). (Contributed by NM, 9-Jul-1994) Reduce axiom dependencies and shorten proof. (Revised by BJ, 7-Oct-2022)

Ref Expression
Hypothesis eubidv.1 φψχ
Assertion eubidv φ∃!xψ∃!xχ

Proof

Step Hyp Ref Expression
1 eubidv.1 φψχ
2 1 alrimiv φxψχ
3 eubi xψχ∃!xψ∃!xχ
4 2 3 syl φ∃!xψ∃!xχ