Theorem pm2.24 622

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		pm2.21 618	. 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 616

This theorem is referenced by:  pm2.24d  623  pm2.53  724  pm2.82  814  pm4.81dc  910  dedlema  972  alexim  1669  eqneqall  2387  elnelall  2484  sotritric  4379  ltxrlt  8158  zltnle  9438  elfzonlteqm1  10361  qltnle  10408  hashfzp1  10991  dfgcd2  12410  oddprmdvds  12752  2lgsoddprm  15665  bj-fast  15816  nnnotnotr  16064