Theorem brcnvssrid 36625

Description: Any set is a converse subset of itself. (Contributed by Peter Mazsa, 9-Jun-2021.)

Assertion

Ref	Expression
brcnvssrid	⊢ (𝐴 ∈ 𝑉 → 𝐴◡ S 𝐴)

Proof of Theorem brcnvssrid

Step	Hyp	Ref	Expression
1		ssid 3943	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brcnvssr 36624	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴◡ S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 257	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴◡ S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2106   ⊆ wss 3887   class class class wbr 5074  ^◡ccnv 5588   S cssr 36336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pr 5352

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-br 5075  df-opab 5137  df-xp 5595  df-rel 5596  df-cnv 5597  df-ssr 36616

This theorem is referenced by: (None)