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Theorem cnvss 4885
 Description: Subset theorem for converse. (Contributed by set.mm contributors, 22-Mar-1998.)
Assertion
Ref Expression
cnvss (A BA B)

Proof of Theorem cnvss
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 3267 . . . 4 (A B → (y, x Ay, x B))
2 df-br 4640 . . . 4 (yAxy, x A)
3 df-br 4640 . . . 4 (yBxy, x B)
41, 2, 33imtr4g 261 . . 3 (A B → (yAxyBx))
54ssopab2dv 4715 . 2 (A B → {x, y yAx} {x, y yBx})
6 df-cnv 4785 . 2 A = {x, y yAx}
7 df-cnv 4785 . 2 B = {x, y yBx}
85, 6, 73sstr4g 3312 1 (A BA B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710   ⊆ wss 3257  ⟨cop 4561  {copab 4622   class class class wbr 4639  ◡ccnv 4771 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623  df-br 4640  df-cnv 4785 This theorem is referenced by:  cnveq  4886  rnss  4959  cnvtr  5098  funss  5126  funcnvuni  5161  funres11  5164  funcnvres  5165  foimacnv  5303
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