Metamath Proof Explorer


Theorem recidd

Description: Multiplication of a number and its reciprocal. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 φ A
reccld.2 φ A 0
Assertion recidd φ A 1 A = 1

Proof

Step Hyp Ref Expression
1 div1d.1 φ A
2 reccld.2 φ A 0
3 recid A A 0 A 1 A = 1
4 1 2 3 syl2anc φ A 1 A = 1