Theorem isanmbfmOLD 34241

Description: Obsolete version of isanmbfm 34243 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 7389	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		mbfmf.3	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3935	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2109  ∪ cuni 4861  ran crn 5624  (class class class)co 7353  sigAlgebracsiga 34094  MblFnMcmbfm 34235

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 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5238  ax-nul 5248  ax-pr 5374

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2066  df-mo 2533  df-eu 2562  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-ral 3045  df-rex 3054  df-rab 3397  df-v 3440  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4479  df-sn 4580  df-pr 4582  df-op 4586  df-uni 4862  df-br 5096  df-opab 5158  df-cnv 5631  df-dm 5633  df-rn 5634  df-iota 6442  df-fv 6494  df-ov 7356

This theorem is referenced by: (None)