Theorem pm2.24 624

Description: Theorem *2.24 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.24	⊢ (𝜑 → (¬ 𝜑 → 𝜓))

Proof of Theorem pm2.24

Step	Hyp	Ref	Expression
1		pm2.21 620	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	com12 30	1 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 618

This theorem is referenced by:  pm2.24d  625  pm2.53  727  pm2.82  817  pm4.81dc  913  dedlema  975  ifp2  986  alexim  1691  eqneqall  2410  elnelall  2507  sotritric  4415  ltxrlt  8220  zltnle  9500  elfzonlteqm1  10424  qltnle  10471  hashfzp1  11054  swrdccat3blem  11279  dfgcd2  12543  oddprmdvds  12885  2lgsoddprm  15800  bj-fast  16129  nnnotnotr  16377