Theorem dff2 100

Description: Alternate definition of "false". (Contributed by NM, 10-Aug-1997.)

Assertion

Ref	Expression
dff2	0 = (a ∪ a⊥ )⊥

Proof of Theorem dff2

Step	Hyp	Ref	Expression
1		df-f 42	. 2 0 = 1⊥
2		df-t 41	. . 3 1 = (a ∪ a⊥ )
3	2	ax-r4 37	. 2 1⊥ = (a ∪ a⊥ )⊥
4	1, 3	ax-r2 36	1 0 = (a ∪ a⊥ )⊥

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  1wt 8  0wf 9

This theorem was proved from axioms:  ax-r2 36  ax-r4 37

This theorem depends on definitions:  df-t 41  df-f 42

This theorem is referenced by:  dff  101  or0  102