Theorem ovsn2 49443

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 49441	. 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 1559   ∈ wcel 2141  Vcvv 3453  {csn 4579  ⟨cotp 4587  (class class class)co 7391

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-10 2174  ax-12 2211  ax-ext 2733  ax-sep 5243  ax-pr 5387

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1099  df-tru 1562  df-fal 1572  df-ex 1799  df-nf 1803  df-sb 2090  df-mo 2565  df-eu 2595  df-clab 2740  df-cleq 2753  df-clel 2836  df-ral 3076  df-rex 3086  df-rab 3414  df-v 3455  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4284  df-if 4478  df-sn 4580  df-pr 4582  df-op 4586  df-ot 4588  df-uni 4863  df-br 5098  df-opab 5160  df-id 5538  df-xp 5649  df-rel 5650  df-cnv 5651  df-co 5652  df-dm 5653  df-iota 6472  df-fun 6518  df-fv 6524  df-ov 7394

This theorem is referenced by:  isinito2lem  50080  isinito3  50082  mndtchom  50166  incat  50183  setc1onsubc  50184