Theorem pm2.24 584

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		pm2.21 580	. 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-1 5  ax-2 6  ax-mp 7  ax-in2 578

This theorem is referenced by:  pm2.24d  585  pm2.53  674  pm2.82  759  pm4.81dc  848  dedlema  911  alexim  1577  eqneqall  2259  sotritric  4114  ltxrlt  7453  zltnle  8690  elfzonlteqm1  9508  qltnle  9544  hashfzp1  10065  dfgcd2  10781