Theorem cnvcnvssOLD 6193

Description: Obsolete version of cnvcnvss 6192 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 6190	. 2 ⊢ ◡◡𝐴 = (𝐴 ∩ (V × V))
2		inss1 4188	. 2 ⊢ (𝐴 ∩ (V × V)) ⊆ 𝐴
3	1, 2	eqsstri 3982	1 ⊢ ◡◡𝐴 ⊆ 𝐴

Syntax hints:  Vcvv 3453   ∩ cin 3903   ⊆ wss 3904   × cxp 5659  ^◡ccnv 5660

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5256  ax-pr 5404

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3415  df-v 3455  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-br 5109  df-opab 5173  df-xp 5667  df-rel 5668  df-cnv 5669

This theorem is referenced by: (None)