Theorem isanmbfmOLD 34256

Description: Obsolete version of isanmbfm 34258 as of 13-Jan-2025. (Contributed by Thierry Arnoux, 30-Jan-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
mbfmf.1	⊢ (𝜑 → 𝑆 ∈ ∪ ran sigAlgebra)
mbfmf.2	⊢ (𝜑 → 𝑇 ∈ ∪ ran sigAlgebra)
mbfmf.3	⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))

Assertion

Ref	Expression
isanmbfmOLD	⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Proof of Theorem isanmbfmOLD

Step	Hyp	Ref	Expression
1		ovssunirn 7467	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		mbfmf.3	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3981	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2108  ∪ cuni 4907  ran crn 5686  (class class class)co 7431  sigAlgebracsiga 34109  MblFnMcmbfm 34250

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-cnv 5693  df-dm 5695  df-rn 5696  df-iota 6514  df-fv 6569  df-ov 7434

This theorem is referenced by: (None)