Theorem brssrid 37978

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 4002	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brssr 37977	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 257	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2098   ⊆ wss 3947   class class class wbr 5150   S cssr 37656

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-sep 5301  ax-nul 5308  ax-pr 5431

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-br 5151  df-opab 5213  df-xp 5686  df-rel 5687  df-ssr 37974

This theorem is referenced by:  issetssr  37979