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Metamath Proof Explorer

Theorem rabeqdv

Description: Equality of restricted class abstractions. Deduction form of rabeq . (Contributed by Glauco Siliprandi, 5-Apr-2020)

Ref Expression
Hypothesis rabeqdv.1 
|- ( ph -> A = B )
Assertion rabeqdv 
|- ( ph -> { x e. A | ps } = { x e. B | ps } )

Proof

Step Hyp Ref Expression
1 rabeqdv.1 
 |-  ( ph -> A = B )
2 rabeq 
 |-  ( A = B -> { x e. A | ps } = { x e. B | ps } )
3 1 2 syl 
 |-  ( ph -> { x e. A | ps } = { x e. B | ps } )