Theorem brssrid 35746

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 3992	. 2 ⊢ 𝐴 ⊆ 𝐴
2		brssr 35745	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 S 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 260	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 S 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2113   ⊆ wss 3939   class class class wbr 5069   S cssr 35460

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 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796  ax-sep 5206  ax-nul 5213  ax-pr 5333

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-mo 2621  df-eu 2653  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-ral 3146  df-rex 3147  df-rab 3150  df-v 3499  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-sn 4571  df-pr 4573  df-op 4577  df-br 5070  df-opab 5132  df-xp 5564  df-rel 5565  df-ssr 35742

This theorem is referenced by:  issetssr  35747