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Theorem funss 5126
 Description: Subclass theorem for function predicate. (The proof was shortened by Mario Carneiro, 24-Jun-2014.) (Contributed by set.mm contributors, 16-Aug-1994.) (Revised by set.mm contributors, 24-Jun-2014.)
Assertion
Ref Expression
funss

Proof of Theorem funss
StepHypRef Expression
1 coss1 4872 . . . 4
2 cnvss 4885 . . . . 5
3 coss2 4873 . . . . 5
42, 3syl 15 . . . 4
51, 4sstrd 3282 . . 3
6 sstr2 3279 . . 3
75, 6syl 15 . 2
8 df-fun 4789 . 2
9 df-fun 4789 . 2
107, 8, 93imtr4g 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wss 3257   ccom 4721   cid 4763  ccnv 4771   wfun 4775 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-co 4726  df-cnv 4785  df-fun 4789 This theorem is referenced by:  funeq  5127  funopab4  5141  funres  5143  funin  5163  funres11  5164  foimacnv  5303
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