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Theorem fssd 4998
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 4997 . 2 ((𝐹:AB B𝐶) → 𝐹:A𝐶)
41, 2, 3syl2anc 391 1 (φ𝐹:A𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2911  wf 4841
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-f 4849
This theorem is referenced by:  fseq1p1m1  8686
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