Theorem tbw-negdf 1532

Description: The definition of negation, in terms of -> and . (Contributed by Anthony Hart, 15-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tbw-negdf

Proof of Theorem tbw-negdf

Step	Hyp	Ref	Expression
1		pm2.21 108	. . 3
2		ax-1 6	. . . . 5
3		falim 1409	. . . . 5
4	2, 3	ja 161	. . . 4
5	4	pm2.43i 47	. . 3
6	1, 5	impbii 188	. 2
7		tbw-bijust 1531	. 2
8	6, 7	mpbi 208	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  wfal 1400

This theorem is referenced by:  re1luk2  1544  re1luk3  1545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-tru 1398  df-fal 1401