Theorem nabi2i 32392

Description: Constructor rule for -/\. (Contributed by Anthony Hart, 2-Sep-2011.)

Hypotheses

Ref	Expression
nabi2i.1	|- ( ph <-> ps )
nabi2i.2	|- ( ch -/\ ps )

Assertion

Ref	Expression
nabi2i	|- ( ch -/\ ph )

Proof of Theorem nabi2i

Step	Hyp	Ref	Expression
1		nabi2i.2	. 2 |- ( ch -/\ ps )
2		nabi2i.1	. . . 4 |- ( ph <-> ps )
3	2	bicomi 214	. . 3 |- ( ps <-> ph )
4	3	nanbi2i 1459	. 2 |- ( ( ch -/\ ps ) <-> ( ch -/\ ph ) )
5	1, 4	mpbi 220	1 |- ( ch -/\ ph )

Syntax hints:   <-> wb 196   -/\ wnan 1447

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 197  df-an 386  df-nan 1448

This theorem is referenced by:  nabi12i  32393