Metamath Proof Explorer


Theorem rspcedvdw

Description: Version of rspcedvd where the implicit substitution hypothesis does not have an antecedent, which also avoids a disjoint variable condition on ph , x . (Contributed by SN, 20-Aug-2024)

Ref Expression
Hypotheses rspcedvdw.s x = A ψ χ
rspcedvdw.1 φ A B
rspcedvdw.2 φ χ
Assertion rspcedvdw φ x B ψ

Proof

Step Hyp Ref Expression
1 rspcedvdw.s x = A ψ χ
2 rspcedvdw.1 φ A B
3 rspcedvdw.2 φ χ
4 1 rspcev A B χ x B ψ
5 2 3 4 syl2anc φ x B ψ