Metamath Proof Explorer


Theorem raleqtrdv

Description: Substitution of equal classes into a restricted universal quantifier. (Contributed by Matthew House, 21-Jul-2025)

Ref Expression
Hypotheses raleqtrdv.1 φ x A ψ
raleqtrdv.2 φ A = B
Assertion raleqtrdv φ x B ψ

Proof

Step Hyp Ref Expression
1 raleqtrdv.1 φ x A ψ
2 raleqtrdv.2 φ A = B
3 2 raleqdv φ x A ψ x B ψ
4 1 3 mpbid φ x B ψ