Metamath Proof Explorer


Theorem mulm1d

Description: Product with minus one is negative. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis mulm1d.1 φA
Assertion mulm1d φ-1A=A

Proof

Step Hyp Ref Expression
1 mulm1d.1 φA
2 mulm1 A-1A=A
3 1 2 syl φ-1A=A