Theorem naim12i 32388

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

Hypotheses

Ref	Expression
naim12i.1	|- ( ph -> ps )
naim12i.2	|- ( ch -> th )
naim12i.3	|- ( ps -/\ th )

Assertion

Ref	Expression
naim12i	|- ( ph -/\ ch )

Proof of Theorem naim12i

Step	Hyp	Ref	Expression
1		naim12i.2	. 2 |- ( ch -> th )
2		naim12i.1	. . 3 |- ( ph -> ps )
3		naim12i.3	. . 3 |- ( ps -/\ th )
4	2, 3	naim1i 32386	. 2 |- ( ph -/\ th )
5	1, 4	naim2i 32387	1 |- ( ph -/\ ch )

Syntax hints:   -> wi 4   -/\ 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-or 385  df-an 386  df-nan 1448

This theorem is referenced by: (None)