Theorem f1ss 5791

Description: A function that is one-to-one is also one-to-one on some superset of its codomain. (Contributed by Mario Carneiro, 12-Jan-2013.)

Assertion

Ref	Expression
f1ss

Proof of Theorem f1ss

Step	Hyp	Ref	Expression
1		f1f 5786	. . 3
2		fss 5744	. . 3
3	1, 2	sylan 471	. 2
4		df-f1 5598	. . . 4
5	4	simprbi 464	. . 3
6	5	adantr 465	. 2
7		df-f1 5598	. 2
8	3, 6, 7	sylanbrc 664	1

Syntax hints:  ->wi 4  /\wa 369  C_wss 3475  `'ccnv 5003  Funwfun 5587  -->wf 5589  -1-1->wf1 5590

This theorem is referenced by:  domssex2  7697  1sdom  7742  marypha1lem  7913  marypha2  7919  isinffi  8394  fseqenlem1  8426  dfac12r  8547  ackbij2  8644  cff1  8659  fin23lem28  8741  fin23lem41  8753  pwfseqlem5  9062  hashf1lem1  12504  gsumzres  16914  gsumzcl2  16915  gsumzf1o  16917  gsumzresOLD  16918  gsumzclOLD  16919  gsumzf1oOLD  16920  gsumzaddlem  16934  gsumzaddlemOLD  16936  gsumzmhm  16957  gsumzmhmOLD  16958  gsumzoppg  16967  gsumzoppgOLD  16968  lindfres  18858  islindf3  18861  dvne0f1  22413  istrkg2ld  23858  ausisusgra  24355  uslisushgra  24363  usisuslgra  24365  uslgra1  24372  usgra1  24373  sizeusglecusglem1  24484  2trllemE  24555  constr1trl  24590  frgrancvvdeqlem8  25040  qqhre  27998  erdsze2lem1  28647  eldioph2lem2  30694  eldioph2  30695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489  df-f 5597  df-f1 5598