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  723  pm2.82  813  pm4.81dc  909  dedlema  971  alexim  1656  eqneqall  2374  elnelall  2471  sotritric  4356  ltxrlt  8087  zltnle  9366  elfzonlteqm1  10280  qltnle  10316  hashfzp1  10898  dfgcd2  12154  oddprmdvds  12495  2lgsoddprm  15270  bj-fast  15303  nnnotnotr  15552