Theorem cnvcnvssOLD 6182

Description: Obsolete version of cnvcnvss 6181 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 6179	. 2 ⊢ ◡◡𝐴 = (𝐴 ∩ (V × V))
2		inss1 4181	. 2 ⊢ (𝐴 ∩ (V × V)) ⊆ 𝐴
3	1, 2	eqsstri 3976	1 ⊢ ◡◡𝐴 ⊆ 𝐴

This proof depends on syntax axioms:  Vcvv 3450   ∩ cin 3897   ⊆ wss 3898   × cxp 5645  ^◡ccnv 5646

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-sep 5248  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4279  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-br 5103  df-opab 5167  df-xp 5653  df-rel 5654  df-cnv 5655

This theorem is used by: (None)