Theorem mt3 204

Description: A rule similar to modus tollens. Inference associated with con1i 148. (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 200	. 2 ⊢ ¬ ¬ 𝜑
4	3	notnotri 132	1 ⊢ 𝜑

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  dfbi1  216  sinhalfpilem  26659  equidq  39731  etransc  47030