Theorem cnvcnvssOLD 6166

Description: Obsolete version of cnvcnvss 6165 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 6163	. 2 ⊢ ◡◡𝐴 = (𝐴 ∩ (V × V))
2		inss1 4179	. 2 ⊢ (𝐴 ∩ (V × V)) ⊆ 𝐴
3	1, 2	eqsstri 3973	1 ⊢ ◡◡𝐴 ⊆ 𝐴

Syntax hints:  Vcvv 3444   ∩ cin 3894   ⊆ wss 3895   × cxp 5634  ^◡ccnv 5635

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-8 2134  ax-9 2142  ax-ext 2724  ax-sep 5236  ax-pr 5380

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-3an 1097  df-tru 1553  df-fal 1563  df-ex 1790  df-sb 2081  df-clab 2731  df-cleq 2744  df-clel 2827  df-rab 3405  df-v 3446  df-dif 3898  df-un 3900  df-in 3902  df-ss 3912  df-nul 4277  df-if 4471  df-sn 4573  df-pr 4575  df-op 4579  df-br 5091  df-opab 5153  df-xp 5642  df-rel 5643  df-cnv 5644

This theorem is referenced by: (None)