Theorem notnotd 592

Description: Deduction associated with notnot 591 and notnoti 606. (Contributed by Jarvin Udandy, 2-Sep-2016.) Avoid biconditional. (Revised by Wolf Lammen, 27-Mar-2021.)

Hypothesis

Ref	Expression
notnotd.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
notnotd	⊢ (𝜑 → ¬ ¬ 𝜓)

Proof of Theorem notnotd

Step	Hyp	Ref	Expression
1		notnotd.1	. 2 ⊢ (𝜑 → 𝜓)
2		notnot 591	. 2 ⊢ (𝜓 → ¬ ¬ 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → ¬ ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 576  ax-in2 577

This theorem is referenced by:  mod2eq1n2dvds  10279