Theorem pm2.24 626

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		pm2.21 622	. 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 620

This theorem is referenced by:  pm2.24d  627  pm2.53  730  pm2.82  820  pm4.81dc  916  dedlema  978  ifp2  989  alexim  1694  eqneqall  2424  elnelall  2521  sotritric  4447  ltxrlt  8344  zltnle  9628  elfzonlteqm1  10562  qltnle  10610  hashfzp1  11197  swrdccat3blem  11439  dfgcd2  12718  oddprmdvds  13060  2lgsoddprm  16035  bj-fast  16562  nnnotnotr  16809