Theorem simplim 143

Description: Simplification. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)

Assertion

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

Proof of Theorem simplim

Step	Hyp	Ref	Expression
1		pm2.21 100	. 2 ⊢ (¬ φ → (φ → ψ))
2	1	con1i 121	1 ⊢ (¬ (φ → 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:  pm2.5  144  pm2.521  146  impt  149  peirce  172  bi1  178  dfbi1  184  pm4.79  566