Theorem mt3 191

Description: A rule similar to modus tollens. Inference associated with con1i 143. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)

Hypotheses

Ref	Expression
mt3.1	⊢ ¬ 𝜓
mt3.2	⊢ (¬ 𝜑 → 𝜓)

Assertion

Ref	Expression
mt3	⊢ 𝜑

Proof of Theorem mt3

Step	Hyp	Ref	Expression
1		mt3.1	. . 3 ⊢ ¬ 𝜓
2		mt3.2	. . 3 ⊢ (¬ 𝜑 → 𝜓)
3	1, 2	mto 187	. 2 ⊢ ¬ ¬ 𝜑
4	3	notnotri 125	1 ⊢ 𝜑

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by:  wfrlem16  7317  sinhalfpilem  24019  equidq  33227  etransc  39176