Theorem fallfacp1d

Description: The value of the falling factorial at a successor. (Contributed by Scott Fenton, 19-Mar-2018)

	Ref	Expression
Hypotheses	rffacp1d.1	|- ( ph -> A e. CC )
	rffacp1d.2	|- ( ph -> N e. NN0 )
Assertion	fallfacp1d	|- ( ph -> ( A FallFac ( N + 1 ) ) = ( ( A FallFac N ) x. ( A - N ) ) )

Proof

Step	Hyp	Ref	Expression
1		rffacp1d.1	|- ( ph -> A e. CC )
2		rffacp1d.2	|- ( ph -> N e. NN0 )
3		fallfacp1	|- ( ( A e. CC /\ N e. NN0 ) -> ( A FallFac ( N + 1 ) ) = ( ( A FallFac N ) x. ( A - N ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( A FallFac ( N + 1 ) ) = ( ( A FallFac N ) x. ( A - N ) ) )