Theorem nicodmpraw 949

Description: The inference rule for the axiom of Nicod, in raw form as explained in nicodraw 948.

Hypotheses

Ref	Expression
nicmin	|- ph
nicmaj	|- -. (ph /\ -. (ch /\ ps))

Assertion

Ref	Expression
nicodmpraw	|- ps

Proof of Theorem nicodmpraw

Step	Hyp	Ref	Expression
1		nicmin	. 2 |- ph
2		nicmaj	. . . 4 |- -. (ph /\ -. (ch /\ ps))
3		iman 237	. . . 4 |- ((ph -> (ch /\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
4	2, 3	mpbir 190	. . 3 |- (ph -> (ch /\ ps))
5	4	pm3.27d 325	. 2 |- (ph -> ps)
6	1, 5	ax-mp 7	1 |- ps

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain