Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Proper substitution of classes for sets into classes
csbieOLD
Metamath Proof Explorer
Description: Obsolete version of csbie as of 15-Oct-2024. (Contributed by AV , 2-Dec-2019) (Proof modification is discouraged.)
(New usage is discouraged.)
Ref
Expression
Hypotheses
csbieOLD.1
⊢ A ∈ V
csbieOLD.2
⊢ x = A → B = C
Assertion
csbieOLD
⊢ ⦋ A / x ⦌ B = C
Proof
Step
Hyp
Ref
Expression
1
csbieOLD.1
⊢ A ∈ V
2
csbieOLD.2
⊢ x = A → B = C
3
nfcv
⊢ Ⅎ _ x C
4
1 3 2
csbief
⊢ ⦋ A / x ⦌ B = C