Theorem pm2.24 630

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		pm2.21 626	. 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 624

This theorem is referenced by:  pm2.24d  631  pm2.53  734  pm2.82  824  pm4.81dc  920  dedlema  982  ifp2  993  alexim  1698  eqneqall  2430  elnelall  2527  sotritric  4467  ltxrlt  8385  zltnle  9673  elfzonlteqm1  10611  qltnle  10661  hashfzp1  11248  swrdccat3blem  11494  dfgcd2  12774  oddprmdvds  13116  2lgsoddprm  16215  bj-fast  16752  nnnotnotr  16999