Theorem brssrid 38213

Description: Any set is a subset of itself. (Contributed by Peter Mazsa, 1-Aug-2019.)

Assertion

Ref	Expression
brssrid	⊢ (𝐴 ∈ 𝑉 → 𝐴 S 𝐴)

Proof of Theorem brssrid

Step	Hyp	Ref	Expression
1		ssid 4001	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brssr 38212	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 257	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2099   ⊆ wss 3946   class class class wbr 5145   S cssr 37892

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697  ax-sep 5296  ax-nul 5303  ax-pr 5425

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3464  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-nul 4323  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-br 5146  df-opab 5208  df-xp 5680  df-rel 5681  df-ssr 38209

This theorem is referenced by:  issetssr  38214