Did all mankind fall in Adam’s first transgression?

The covenant being made with Adam, not only for himself, but for his posterity; all mankind, descending from him by ordinary generation, sinned in him, and fell with him, in his first transgression.

Proofs

• The covenant being made with Adam, not only for himself, but for his posterity; all mankind, descending from him by ordinary generation, sinned in him, and fell with him, in his first transgression. (Genesis 2:16–17; Romans 5:12; 1 Corinthians 15:21–22)