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Database ZF (ZERMELO-FRAENKEL) SET THEORY ZF Set Theory - add the Axiom of Replacement Theorems requiring subset and intersection existence rabexgOLD
Description: Obsolete version of rabexg as of 24-Jul-2025). (Contributed by NM , 23-Oct-1999) (Proof modification is discouraged.)
(New usage is discouraged.)
Ref
Expression
Assertion
rabexgOLD ⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )
Proof
Step
Hyp
Ref
Expression
1
ssrab2 ⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴
2
ssexg ⊢ ( ( { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴 ∧ 𝐴 ∈ 𝑉 ) → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )
3
1 2
mpan ⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )