Metamath Proof Explorer

Theorem spimvw

Description: A weak form of specialization. Lemma 8 of KalishMontague p. 87. Uses only Tarski's FOL axiom schemes. For stronger forms using more axioms, see spimv and spimfv . (Contributed by NM, 9-Apr-2017)

Ref Expression
Hypothesis spimvw.1 x = y φ ψ
Assertion spimvw x φ ψ


Step Hyp Ref Expression
1 spimvw.1 x = y φ ψ
2 ax-5 ¬ ψ x ¬ ψ
3 2 1 spimw x φ ψ