Metamath Proof Explorer


Theorem jm2.27dlem5

Description: Lemma for rmydioph . Used with sselii to infer membership of midpoints of range; jm2.27dlem2 is deprecated. (Contributed by Stefan O'Rear, 11-Oct-2014)

Ref Expression
Hypotheses jm2.27dlem5.2
|- B = ( A + 1 )
jm2.27dlem5.3
|- ( 1 ... B ) C_ ( 1 ... C )
Assertion jm2.27dlem5
|- ( 1 ... A ) C_ ( 1 ... C )

Proof

Step Hyp Ref Expression
1 jm2.27dlem5.2
 |-  B = ( A + 1 )
2 jm2.27dlem5.3
 |-  ( 1 ... B ) C_ ( 1 ... C )
3 fzssp1
 |-  ( 1 ... A ) C_ ( 1 ... ( A + 1 ) )
4 1 oveq2i
 |-  ( 1 ... B ) = ( 1 ... ( A + 1 ) )
5 3 4 sseqtrri
 |-  ( 1 ... A ) C_ ( 1 ... B )
6 5 2 sstri
 |-  ( 1 ... A ) C_ ( 1 ... C )