Theorem isanmbfmOLD 34235

Description: Obsolete version of isanmbfm 34237 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 7466	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		mbfmf.3	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3992	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2105  ∪ cuni 4911  ran crn 5689  (class class class)co 7430  sigAlgebracsiga 34088  MblFnMcmbfm 34229

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-10 2138  ax-11 2154  ax-12 2174  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pr 5437

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-nf 1780  df-sb 2062  df-mo 2537  df-eu 2566  df-clab 2712  df-cleq 2726  df-clel 2813  df-ne 2938  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-opab 5210  df-cnv 5696  df-dm 5698  df-rn 5699  df-iota 6515  df-fv 6570  df-ov 7433

This theorem is referenced by: (None)