Metamath Proof Explorer


Theorem ss2rabdf

Description: Deduction of restricted abstraction subclass from implication. (Contributed by Glauco Siliprandi, 21-Dec-2024)

Ref Expression
Hypotheses ss2rabdf.1 x φ
ss2rabdf.2 φ x A ψ χ
Assertion ss2rabdf φ x A | ψ x A | χ

Proof

Step Hyp Ref Expression
1 ss2rabdf.1 x φ
2 ss2rabdf.2 φ x A ψ χ
3 2 ex φ x A ψ χ
4 1 3 ralrimi φ x A ψ χ
5 ss2rab x A | ψ x A | χ x A ψ χ
6 4 5 sylibr φ x A | ψ x A | χ