Theorem pm2.24 621

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		pm2.21 617	. 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 615

This theorem is referenced by:  pm2.24d  622  pm2.53  722  pm2.82  812  pm4.81dc  908  dedlema  969  alexim  1645  eqneqall  2357  elnelall  2454  sotritric  4324  ltxrlt  8022  zltnle  9298  elfzonlteqm1  10209  qltnle  10245  hashfzp1  10803  dfgcd2  12014  oddprmdvds  12351  bj-fast  14463  nnnotnotr  14712