Theorem bj-imnimnn 13629

Description: If a formula is implied by both a formula and its negation, then it is not refutable. There is another proof using the inference associated with bj-nnclavius 13628 as its last step. (Contributed by BJ, 27-Oct-2024.)

Hypotheses

Ref	Expression
bj-imnimnn.1	|- ( ph -> ps )
bj-imnimnn.2	|- ( -. ph -> ps )

Assertion

Ref	Expression
bj-imnimnn	|- -. -. ps

Proof of Theorem bj-imnimnn

Step	Hyp	Ref	Expression
1		bj-imnimnn.1	. . 3 |- ( ph -> ps )
2	1	con3i 622	. 2 |- ( -. ps -> -. ph )
3		bj-imnimnn.2	. . 3 |- ( -. ph -> ps )
4	3	con3i 622	. 2 |- ( -. ps -> -. -. ph )
5	2, 4	pm2.65i 629	1 |- -. -. ps

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605

This theorem is referenced by:  bj-nnst  13634