Theorem simplim 168

Description: Simplification. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-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		pm2.21 124	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	con1i 148	1 ⊢ (¬ (𝜑 → 𝜓) → 𝜑)

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:  pm2.5g  169  pm2.521g2  176  impt  180  peirce  205  biimp  218  imbi12  349  pm4.79  1021  antnest  36375  antnestlaw3lem  36376  antnestlaw2  36378  mptbi12f  39018  ac6s6  39024  rp-fakeimass  44456