Theorem mt4 117

Description: The rule of modus tollens. Inference associated with con4i 115. (Contributed by Wolf Lammen, 12-May-2013.)

Hypotheses

Ref	Expression
mt4.1	⊢ 𝜑
mt4.2	⊢ (¬ 𝜓 → ¬ 𝜑)

Assertion

Ref	Expression
mt4	⊢ 𝜓

Proof of Theorem mt4

Step	Hyp	Ref	Expression
1		mt4.1	. 2 ⊢ 𝜑
2		mt4.2	. . 3 ⊢ (¬ 𝜓 → ¬ 𝜑)
3	2	con4i 115	. 2 ⊢ (𝜑 → 𝜓)
4	1, 3	ax-mp 5	1 ⊢ 𝜓

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

This proof depends on axioms:  ax-mp 5  ax-3 8

This theorem is used by:  notnotri  132  infeq5i  9615  chirredi  32783