Theorem con4iOLD 144

Description: Obsolete proof of con4i 112 as of 15-Jul-2021. This shorter proof has been reverted to its original to avoid a dependency on ax-1 6 and ax-2 7. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 21-Jun-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
con4iOLD.1	⊢ (¬ 𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
con4iOLD	⊢ (𝜓 → 𝜑)

Proof of Theorem con4iOLD

Step	Hyp	Ref	Expression
1		notnot 135	. 2 ⊢ (𝜓 → ¬ ¬ 𝜓)
2		con4iOLD.1	. 2 ⊢ (¬ 𝜑 → ¬ 𝜓)
3	1, 2	nsyl2 141	1 ⊢ (𝜓 → 𝜑)

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: (None)