Theorem cnvcnvssOLD 6181

Description: Obsolete version of cnvcnvss 6180 as of 10-Jun-2026. (Contributed by NM, 23-Jul-2004.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
cnvcnvssOLD	⊢ ◡◡𝐴 ⊆ 𝐴

Proof of Theorem cnvcnvssOLD

Step	Hyp	Ref	Expression
1		cnvcnv 6178	. 2 ⊢ ◡◡𝐴 = (𝐴 ∩ (V × V))
2		inss1 4189	. 2 ⊢ (𝐴 ∩ (V × V)) ⊆ 𝐴
3	1, 2	eqsstri 3983	1 ⊢ ◡◡𝐴 ⊆ 𝐴

Syntax hints:  Vcvv 3455   ∩ cin 3904   ⊆ wss 3905   × cxp 5646  ^◡ccnv 5647

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5247  ax-pr 5391

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1564  df-fal 1574  df-ex 1801  df-sb 2092  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-br 5102  df-opab 5164  df-xp 5654  df-rel 5655  df-cnv 5656

This theorem is referenced by: (None)