Confusion about assignment axiom in Hoare logic
The assignment axiom in standard Hoare logic says:

|- {P[e/x]}x:=e{P}

If you choose P[e/x] to be x+1=44 (that is e is x+1) you get:

|- {x+1=44} x:=x+1 {x=44}

By the consequence rule, since: 
|= x=43 --> x+1=44, and 
|= x+1=44 --> x+1=44, and
|- {x+1=44} x:=x+1 {x=44} 

you know that |- {x=43} x:=x+1 {x=44} .

By soundness: 
|={x=43} x:=x+1 {x=44}