Theorem notnotd 145

Description: Deduction associated with notnot 143 and notnoti 144. (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 143	. 2 ⊢ (𝜓 → ¬ ¬ 𝜓)
3	1, 2	syl 18	1 ⊢ (𝜑 → ¬ ¬ 𝜓)

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:  eupth2lemb  30528  xrdifh  33065  aks6d1c5  42795  aks6d1c6lem3  42828  nnfoctbdjlem  47060  lighneallem1  48245  lighneallem3  48247  lindslinindsimp2  49127