Theorem ifpn 1391

Description: Conditional operator for the negation of a proposition. (Contributed by BJ, 30-Sep-2019.)

Assertion

Ref	Expression
ifpn

Proof of Theorem ifpn

Step	Hyp	Ref	Expression
1		notnot 291	. . . 4
2	1	imbi1i 325	. . 3
3	2	anbi2ci 696	. 2
4		dfifp2 1382	. 2
5		dfifp2 1382	. 2
6	3, 4, 5	3bitr4i 277	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  if-wif 1380

This theorem is referenced by:  bj-ifdfbi  37730

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-or 370  df-an 371  df-ifp 1381