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Theorem funres11 5235
 Description: The restriction of a one-to-one function is one-to-one. (Contributed by NM, 25-Mar-1998.)
Assertion
Ref Expression
funres11

Proof of Theorem funres11
StepHypRef Expression
1 resss 4883 . 2
2 cnvss 4752 . 2
3 funss 5182 . 2
41, 2, 3mp2b 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wss 3098  ccnv 4578   cres 4581   wfun 5157 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-in 3104  df-ss 3111  df-br 3962  df-opab 4022  df-rel 4586  df-cnv 4587  df-co 4588  df-res 4591  df-fun 5165 This theorem is referenced by:  f1ssres  5377  resdif  5429  ssdomg  6712  sbthlemi8  6897
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