Theorem isanmbfmOLD 33930

Description: Obsolete version of isanmbfm 33932 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 7451	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		mbfmf.3	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3970	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2098  ∪ cuni 4903  ran crn 5673  (class class class)co 7415  sigAlgebracsiga 33783  MblFnMcmbfm 33924

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696  ax-sep 5294  ax-nul 5301  ax-pr 5423

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2931  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3465  df-dif 3943  df-un 3945  df-ss 3957  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4904  df-br 5144  df-opab 5206  df-cnv 5680  df-dm 5682  df-rn 5683  df-iota 6494  df-fv 6550  df-ov 7418

This theorem is referenced by: (None)