Section 6.13 蕴含式中量词辖域的扩张
设公式A中含x, 公式B中不含x
Objectives: B在左边的情况
- \(\displaystyle B \imp \forall x A(x) \Iff \forall x (B \imp A(x)) \)
- \(\displaystyle B \imp \exists x A(x) \Iff \exists x(B \imp A(x)) \)
Objectives: B在右边的情况
- \(\displaystyle \exists x A(x) \imp B \Iff \forall x (A(x) \imp B) \)
- \(\displaystyle \forall x A(x) \imp B \Iff \exists x (A(x) \imp B)\)