Theorem ovsn2 49106

Description: The operation value of a singleton of an ordered triple is the last member. (Contributed by Zhi Wang, 22-Oct-2025.)

Hypothesis

Ref	Expression
ovsn.1	⊢ 𝐶 ∈ V

Assertion

Ref	Expression
ovsn2	⊢ (𝐴{⟨𝐴, 𝐵, 𝐶⟩}𝐵) = 𝐶

Proof of Theorem ovsn2

Step	Hyp	Ref	Expression
1		ovsn.1	. 2 ⊢ 𝐶 ∈ V
2		ovsng2 49104	. 2 ⊢ (𝐶 ∈ V → (𝐴{⟨𝐴, 𝐵, 𝐶⟩}𝐵) = 𝐶)
3	1, 2	ax-mp 5	1 ⊢ (𝐴{⟨𝐴, 𝐵, 𝐶⟩}𝐵) = 𝐶

Syntax hints:   = wceq 1541   ∈ wcel 2113  Vcvv 3440  {csn 4580  ⟨cotp 4588  (class class class)co 7358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-10 2146  ax-12 2184  ax-ext 2708  ax-sep 5241  ax-nul 5251  ax-pr 5377

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2539  df-eu 2569  df-clab 2715  df-cleq 2728  df-clel 2811  df-ral 3052  df-rex 3061  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-ot 4589  df-uni 4864  df-br 5099  df-opab 5161  df-id 5519  df-xp 5630  df-rel 5631  df-cnv 5632  df-co 5633  df-dm 5634  df-iota 6448  df-fun 6494  df-fv 6500  df-ov 7361

This theorem is referenced by:  isinito2lem  49743  isinito3  49745  mndtchom  49829  incat  49846  setc1onsubc  49847