Theorem brssrid 38478

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 3960	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brssr 38477	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 258	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2109   ⊆ wss 3905   class class class wbr 5095   S cssr 38157

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5238  ax-nul 5248  ax-pr 5374

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ral 3045  df-rex 3054  df-rab 3397  df-v 3440  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4479  df-sn 4580  df-pr 4582  df-op 4586  df-br 5096  df-opab 5158  df-xp 5629  df-rel 5630  df-ssr 38474

This theorem is referenced by:  issetssr  38479