Theorem pm2.621 423

Description: Theorem *2.621 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.621	⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))

Proof of Theorem pm2.621

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2		idd 24	. 2 ⊢ ((𝜑 → 𝜓) → (𝜓 → 𝜓))
3	1, 2	jaod 394	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))

Syntax hints:   → wi 4   ∨ wo 382

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-or 384

This theorem is referenced by:  pm2.62  424  pm2.73  886  pm4.72  916  undif4  3987  elnn1uz2  11641