Description: Equality theorem for negatives. (Contributed by NM, 10-Feb-1995)
Ref | Expression | ||
---|---|---|---|
Assertion | negeq | $${\u22a2}{A}={B}\to -{A}=-{B}$$ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 | $${\u22a2}{A}={B}\to 0-{A}=0-{B}$$ | |
2 | df-neg | $${\u22a2}-{A}=0-{A}$$ | |
3 | df-neg | $${\u22a2}-{B}=0-{B}$$ | |
4 | 1 2 3 | 3eqtr4g | $${\u22a2}{A}={B}\to -{A}=-{B}$$ |