Theorem pm2.5g 169

Description: General instance of Theorem *2.5 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 9-Oct-2012.)

Assertion

Ref	Expression
pm2.5g	⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜒))

Proof of Theorem pm2.5g

Step	Hyp	Ref	Expression
1		simplim 168	. 2 ⊢ (¬ (𝜑 → 𝜓) → 𝜑)
2	1	pm2.24d 152	1 ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜒))

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:  pm2.5  170  pm5.11g  958