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Theorem fssd 5397
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 5396 . 2 ((𝐹:𝐴𝐵𝐵𝐶) → 𝐹:𝐴𝐶)
41, 2, 3syl2anc 411 1 (𝜑𝐹:𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3144  wf 5231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157  df-f 5239
This theorem is referenced by:  mapss  6718  ac6sfi  6927  fseq1p1m1  10126  resqrexlemcvg  11063  resqrexlemsqa  11068  climcvg1nlem  11392  fsumcl2lem  11441  ennnfonelemh  12458  gsumress  12873  cnrest2  14213  cnptoprest2  14217  cncfss  14547  limccnpcntop  14621  dvcoapbr  14648  dvef  14665  isomninnlem  15257  trilpolemisumle  15265  iswomninnlem  15276  ismkvnnlem  15279
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