Metamath Proof Explorer


Theorem 4ralbidv

Description: Formula-building rule for restricted universal quantifiers (deduction form.) (Contributed by Scott Fenton, 20-Feb-2025)

Ref Expression
Hypothesis 4ralbidv.1 φ ψ χ
Assertion 4ralbidv φ x A y B z C w D ψ x A y B z C w D χ

Proof

Step Hyp Ref Expression
1 4ralbidv.1 φ ψ χ
2 1 ralbidv φ w D ψ w D χ
3 2 3ralbidv φ x A y B z C w D ψ x A y B z C w D χ