Metamath Proof Explorer

Theorem cbv3hv

Description: Rule used to change bound variables, using implicit substitution. Version of cbv3h with a disjoint variable condition on x , y , which does not require ax-13 . Was used in a proof of axc11n (but of independent interest). (Contributed by NM, 25-Jul-2015) (Proof shortened by Wolf Lammen, 29-Nov-2020) (Proof shortened by BJ, 30-Nov-2020)

Ref Expression
Hypotheses cbv3hv.nf1 φ y φ
cbv3hv.nf2 ψ x ψ
cbv3hv.1 x = y φ ψ
Assertion cbv3hv x φ y ψ


Step Hyp Ref Expression
1 cbv3hv.nf1 φ y φ
2 cbv3hv.nf2 ψ x ψ
3 cbv3hv.1 x = y φ ψ
4 1 nf5i y φ
5 2 nf5i x ψ
6 4 5 3 cbv3v x φ y ψ