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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	$⊢ \neg \neg φ$
	Assertion	notnotriALT	$⊢ φ$

Proof

Step	Hyp	Ref	Expression
1		notnotri.1	$⊢ \neg \neg φ$
2	1	pm2.21i	$⊢ \neg φ \to φ$
3	2	pm2.18i	$⊢ φ$