`rArr` and `hArr` are not propositional operators

- different syntax:

`(2x-6 = 0 harr 2x = 6) harr x = 3` is the same as

`2x-6 = 0 harr 2x = 6 harr x = 3`

`(2x-6 = 0 hArr 2x = 6) hArr x = 3` is a syntax error - so negation cannot be applied to `rArr` and
`hArr`

- different meaning of chains:

`2x-6 = 0 hArr 2x = 6 hArr x = 3` is valid for every `x in RR`

`2x-6 = 0 harr 2x = 6 harr x = 3` yields**F**when `x ne 3`

- different reaction to context information

case `x < 0`: … `x^2 = 9 hArr x = -3`

- `sqrt(x) = 2 hArr x=4` yields it when `x = -1`
`rArr` **F****U****T**`hArr` **F****U****T****F**✓ ✓ ✓ **F**✓ ✓ – **U**✓ ✓ ✓ **U**✓ ✓ – **T**– – ✓ **T**– – ✓