Tying TRUE or FALSE Formulas Together

Hello,
Can anyone help me develop a formula for the following setup?

A1: 5
A2: 6
A3: 9
A4: 7

B1:=IF(A1<A2,TRUE,FALSE)
B2:=IF(A3>A4,TRUE,FALSE)

I need a formula that's added to B2 that only applies it's formula if B1 is TRUE. So if B1 is false due to a change in value of A1 or A2 and now the statement is false, B2 is BLANK or FALSE it's self no matter if it's TRUE or not. Thanks in advance for any and all help.

In B1, =A1<A2

In B2, =AND(B1, A3>A4)