Let $$a = b$$ $$c = d$$
Assume a,b,c,d are non-zeros
If we know that $$\frac{a}{c} = \frac{b}{d}$$
Are the original equations valid? I know we can arrive at a true statement from false statements so even if original equations are not valid, the derived equation can be valid, right? I'm still confused tho because there is not really any logical mistakes in steps that could lead to a true statement from two false statements in this case.
Thanks in advance.