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Theorem fssd 5221
Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
fssd.f (𝜑𝐹:𝐴𝐵)
fssd.b (𝜑𝐵𝐶)
Assertion
Ref Expression
fssd (𝜑𝐹:𝐴𝐶)

Proof of Theorem fssd
StepHypRef Expression
1 fssd.f . 2 (𝜑𝐹:𝐴𝐵)
2 fssd.b . 2 (𝜑𝐵𝐶)
3 fss 5220 . 2 ((𝐹:𝐴𝐵𝐵𝐶) → 𝐹:𝐴𝐶)
41, 2, 3syl2anc 406 1 (𝜑𝐹:𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3021  wf 5055
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-11 1452  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-in 3027  df-ss 3034  df-f 5063
This theorem is referenced by:  mapss  6515  ac6sfi  6721  fseq1p1m1  9715  resqrexlemcvg  10631  resqrexlemsqa  10636  climcvg1nlem  10957  fsumcl2lem  11006  ennnfonelemh  11709  cnrest2  12186  cnptoprest2  12190  cncfss  12483  limccnpcntop  12520  isomninnlem  12809  trilpolemisumle  12815
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