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Theorem fssd 5380
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 5379 . 2 ((𝐹:𝐴𝐵𝐵𝐶) → 𝐹:𝐴𝐶)
41, 2, 3syl2anc 411 1 (𝜑𝐹:𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3131  wf 5214
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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3137  df-ss 3144  df-f 5222
This theorem is referenced by:  mapss  6693  ac6sfi  6900  fseq1p1m1  10096  resqrexlemcvg  11030  resqrexlemsqa  11035  climcvg1nlem  11359  fsumcl2lem  11408  ennnfonelemh  12407  cnrest2  13775  cnptoprest2  13779  cncfss  14109  limccnpcntop  14183  dvcoapbr  14210  dvef  14227  isomninnlem  14817  trilpolemisumle  14825  iswomninnlem  14836  ismkvnnlem  14839
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