Theorem nabi1i 32391

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

Hypotheses

Ref	Expression
nabi1i.1	|- ( ph <-> ps )
nabi1i.2	|- ( ps -/\ ch )

Assertion

Ref	Expression
nabi1i	|- ( ph -/\ ch )

Proof of Theorem nabi1i

Step	Hyp	Ref	Expression
1		nabi1i.2	. 2 |- ( ps -/\ ch )
2		nabi1i.1	. . . 4 |- ( ph <-> ps )
3	2	bicomi 214	. . 3 |- ( ps <-> ph )
4	3	nanbi1i 1458	. 2 |- ( ( ps -/\ ch ) <-> ( ph -/\ ch ) )
5	1, 4	mpbi 220	1 |- ( ph -/\ ch )

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