Theorem brcnvssrid 38961

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 3944	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brcnvssr 38960	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴◡ S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 259	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴◡ S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2119   ⊆ wss 3890   class class class wbr 5079  ^◡ccnv 5624   S cssr 38560

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-sep 5225  ax-pr 5369

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ral 3055  df-rex 3065  df-rab 3393  df-v 3434  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-br 5080  df-opab 5142  df-xp 5631  df-rel 5632  df-cnv 5633  df-ssr 38952

This theorem is referenced by: (None)