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)

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:  eupth2lemb  30659  xrdifh  33195  aks6d1c5  42964  aks6d1c6lem3  42997  nnfoctbdjlem  47227  lighneallem1  48415  lighneallem3  48417  lindslinindsimp2  49300