Metamath Proof Explorer

Theorem cbvaldw

Description: Deduction used to change bound variables, using implicit substitution. Version of cbvald with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 2-Jan-2002) (Revised by Gino Giotto, 10-Jan-2024)

Ref Expression
Hypotheses cbvaldw.1 y φ
cbvaldw.2 φ y ψ
cbvaldw.3 φ x = y ψ χ
Assertion cbvaldw φ x ψ y χ


Step Hyp Ref Expression
1 cbvaldw.1 y φ
2 cbvaldw.2 φ y ψ
3 cbvaldw.3 φ x = y ψ χ
4 nfv x φ
5 nfvd φ x χ
6 4 1 2 5 3 cbv2w φ x ψ y χ