Theorem fssd 4998

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

Step	Hyp	Ref	Expression
1		fssd.f	. 2 |- (ph -> F :A -->B)
2		fssd.b	. 2 |- (ph -> B C_ C)
3		fss 4997	. 2 |- (( F :A -->B /\ B C_ C) -> F :A --> C)
4	1, 2, 3	syl2anc 391	1 |- (ph -> F :A --> C)

Syntax hints:   -> wi 4   C_ 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  8726