Metamath Proof Explorer

Theorem cbvald

Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim . Usage of this theorem is discouraged because it depends on ax-13 . See cbvaldw for a version with x , y disjoint, not depending on ax-13 . (Contributed by NM, 2-Jan-2002) (Revised by Mario Carneiro, 6-Oct-2016) (Revised by Wolf Lammen, 13-May-2018) (New usage is discouraged.)

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


Step Hyp Ref Expression
1 cbvald.1 y φ
2 cbvald.2 φ y ψ
3 cbvald.3 φ x = y ψ χ
4 nfv x φ
5 nfvd φ x χ
6 4 1 2 5 3 cbv2 φ x ψ y χ