Theorem pm2.621 912

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 23	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2		idd 25	. 2 ⊢ ((𝜑 → 𝜓) → (𝜓 → 𝜓))
3	1, 2	jaod 873	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  pm2.62  913  pm4.72  964  pm2.73  989  undif4  4430  elnn1uz2  12967