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Theorem fssd 5086
Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
fssd.f  |-  ( ph  ->  F : A --> B )
fssd.b  |-  ( ph  ->  B  C_  C )
Assertion
Ref Expression
fssd  |-  ( ph  ->  F : A --> C )

Proof of Theorem fssd
StepHypRef Expression
1 fssd.f . 2  |-  ( ph  ->  F : A --> B )
2 fssd.b . 2  |-  ( ph  ->  B  C_  C )
3 fss 5085 . 2  |-  ( ( F : A --> B  /\  B  C_  C )  ->  F : A --> C )
41, 2, 3syl2anc 403 1  |-  ( ph  ->  F : A --> C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 2974   -->wf 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-f 4936
This theorem is referenced by:  ac6sfi  6431  fseq1p1m1  9187  resqrexlemcvg  10043  resqrexlemsqa  10048  climcvg1nlem  10324
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