Theorem ovsn2 48837

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 48835	. 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 1540   ∈ wcel 2109  Vcvv 3450  {csn 4591  ⟨cotp 4599  (class class class)co 7389

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-12 2178  ax-ext 2702  ax-sep 5253  ax-nul 5263  ax-pr 5389

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 2534  df-eu 2563  df-clab 2709  df-cleq 2722  df-clel 2804  df-ral 3046  df-rex 3055  df-rab 3409  df-v 3452  df-dif 3919  df-un 3921  df-ss 3933  df-nul 4299  df-if 4491  df-sn 4592  df-pr 4594  df-op 4598  df-ot 4600  df-uni 4874  df-br 5110  df-opab 5172  df-id 5535  df-xp 5646  df-rel 5647  df-cnv 5648  df-co 5649  df-dm 5650  df-iota 6466  df-fun 6515  df-fv 6521  df-ov 7392

This theorem is referenced by:  isinito2lem  49467  isinito3  49469  mndtchom  49553  incat  49570  setc1onsubc  49571