Metamath Proof Explorer


Theorem notnotriALT

Description: Alternate proof of notnotri . The proof via notnotr and ax-mp also has three essential steps, but has a total number of steps equal to 8, instead of the present 7, because it has to construct the formula ph twice and the formula -. -. ph once, whereas the present proof has to construct the formula ph twice and the formula -. ph once, and therefore makes only one use of wn instead of two. This can be checked by running the Metamath command "MM> SHOW PROOF notnotri / NORMAL". (Contributed by NM, 27-Feb-2008) (Proof shortened by Wolf Lammen, 15-Jul-2021) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis notnotri.1 ¬ ¬ φ
Assertion notnotriALT φ

Proof

Step Hyp Ref Expression
1 notnotri.1 ¬ ¬ φ
2 1 pm2.21i ¬ φ φ
3 2 pm2.18i φ