Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Restricted quantification
rspa
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rspec
Metamath Proof Explorer
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Unicode
Theorem
rspa
Description:
Restricted specialization.
(Contributed by
Glauco Siliprandi
, 11-Dec-2019)
Ref
Expression
Assertion
rspa
⊢
∀
x
∈
A
φ
∧
x
∈
A
→
φ
Proof
Step
Hyp
Ref
Expression
1
rsp
⊢
∀
x
∈
A
φ
→
x
∈
A
→
φ
2
1
imp
⊢
∀
x
∈
A
φ
∧
x
∈
A
→
φ