Metamath Proof Explorer


Theorem uniabio

Description: Part of Theorem 8.17 in Quine p. 56. This theorem serves as a lemma for the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011)

Ref Expression
Assertion uniabio x φ x = y x | φ = y

Proof

Step Hyp Ref Expression
1 abbi1 x φ x = y x | φ = x | x = y
2 df-sn y = x | x = y
3 1 2 syl6eqr x φ x = y x | φ = y
4 3 unieqd x φ x = y x | φ = y
5 vex y V
6 5 unisn y = y
7 4 6 syl6eq x φ x = y x | φ = y