Theorem isanmbfmOLD

Description: Obsolete version of isanmbfm as of 13-Jan-2025. (Contributed by Thierry Arnoux, 30-Jan-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	mbfmf.1	⊢ ( 𝜑 → 𝑆 ∈ ∪ ran sigAlgebra )
	mbfmf.2	⊢ ( 𝜑 → 𝑇 ∈ ∪ ran sigAlgebra )
	mbfmf.3	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 MblFnM 𝑇 ) )
Assertion	isanmbfmOLD	⊢ ( 𝜑 → 𝐹 ∈ ∪ ran MblFnM )

Proof

Step	Hyp	Ref	Expression
1		mbfmf.1	⊢ ( 𝜑 → 𝑆 ∈ ∪ ran sigAlgebra )
2		mbfmf.2	⊢ ( 𝜑 → 𝑇 ∈ ∪ ran sigAlgebra )
3		mbfmf.3	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 MblFnM 𝑇 ) )
4		ovssunirn	⊢ ( 𝑆 MblFnM 𝑇 ) ⊆ ∪ ran MblFnM
5	4 3	sselid	⊢ ( 𝜑 → 𝐹 ∈ ∪ ran MblFnM )