Theorem nabi12i 32393

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

Hypotheses

Ref	Expression
nabi12i.1	|- ( ph <-> ps )
nabi12i.2	|- ( ch <-> th )
nabi12i.3	|- ( ps -/\ th )

Assertion

Ref	Expression
nabi12i	|- ( ph -/\ ch )

Proof of Theorem nabi12i

Step	Hyp	Ref	Expression
1		nabi12i.2	. 2 |- ( ch <-> th )
2		nabi12i.1	. . 3 |- ( ph <-> ps )
3		nabi12i.3	. . 3 |- ( ps -/\ th )
4	2, 3	nabi1i 32391	. 2 |- ( ph -/\ th )
5	1, 4	nabi2i 32392	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: (None)