Theorem jcn 162

Description: Theorem joining the consequents of two premises. Theorem 8 of [Margaris] p. 60. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Assertion

Ref	Expression
jcn	⊢ (𝜑 → (¬ 𝜓 → ¬ (𝜑 → 𝜓)))

Proof of Theorem jcn

Step	Hyp	Ref	Expression
1		pm2.27 42	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
2	1	con3d 152	1 ⊢ (𝜑 → (¬ 𝜓 → ¬ (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:  jcnd  163  jath  33672  nmotru  34597  meran1  34600  onpsstopbas  34619  bj-brrelex12ALT  35238