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  4419  ltxrlt  8238  zltnle  9518  elfzonlteqm1  10448  qltnle  10496  hashfzp1  11081  swrdccat3blem  11313  dfgcd2  12578  oddprmdvds  12920  2lgsoddprm  15835  bj-fast  16287  nnnotnotr  16535