Metamath Proof Explorer

Theorem spime

Description: Existential introduction, using implicit substitution. Compare Lemma 14 of Tarski p. 70. Usage of this theorem is discouraged because it depends on ax-13 . Check out spimew for a weaker version requiring less axioms. (Contributed by NM, 7-Aug-1994) (Revised by Mario Carneiro, 3-Oct-2016) (Proof shortened by Wolf Lammen, 6-Mar-2018) (New usage is discouraged.)

Ref Expression
Hypotheses spime.1 x φ
spime.2 x = y φ ψ
Assertion spime φ x ψ


Step Hyp Ref Expression
1 spime.1 x φ
2 spime.2 x = y φ ψ
3 1 a1i x φ
4 3 2 spimed φ x ψ
5 4 mptru φ x ψ