Theorem notnotriALT 132

Description: Alternate proof of notnotri 131. The proof via notnotr 130 and ax-mp 5 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 𝜑 twice and the formula ¬ ¬ 𝜑 once, whereas the present proof has to construct the formula 𝜑 twice and the formula ¬ 𝜑 once, and therefore makes only one use of wn 3 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.)

Hypothesis

Ref	Expression
notnotri.1	⊢ ¬ ¬ 𝜑

Assertion

Ref	Expression
notnotriALT	⊢ 𝜑

Proof of Theorem notnotriALT

Step	Hyp	Ref	Expression
1		notnotri.1	. . 3 ⊢ ¬ ¬ 𝜑
2	1	pm2.21i 119	. 2 ⊢ (¬ 𝜑 → 𝜑)
3	2	pm2.18i 129	1 ⊢ 𝜑

Syntax hints:  ¬ wn 3

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)