A Truth Table with Connectives as Variables

I will use a truth table to deduce that REL in XXXX REL Yyyy is equivalent to ↑ as if ↑ were a variable.

0110  	1000  	↑	0110 ↑ 1000		↑ ↔ (0110 ↑ 1000)

0		0		1	1				1
0		1		1	1				1
1		0		1	1				1
1		1		0	0				1

It appears to me that logicians do not intend connectives to be used as variables like that. But according to this same proof method:

1001	0110	0001	↔ ⊻ ∧	1001 ↔ 1001		1001 ⊻ 0110		1001 ∧ 0001

0		0		0		1 0 0	1				0				0
0		0		1		0 1 0									0
0		1		0		0 1 0					1
0		1		1		1 0 1
1		0		0				1				1				0
1		0		1												1
1		1		0								0
1		1		1

Therefore we can abbreviate 1001 ⊻ 0110 as ⊻ and 1001 ∧ 0001 as ∧ and state:

⊻ ∧ ↑ 	⊻ ↑ ∧	↑ ↔ (⊻ ↑ ∧)

0 0 1	1		1
0 1 1	1		1
1 0 1	1		1
1 1 0	0		1

Which reinforces the hypothesis that connectives can be used as variables like this.