Theorem pm2.621 737

Description: Theorem *2.621 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 13-Dec-2013.)

Assertion

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

Proof of Theorem pm2.621

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2		idd 21	. 2 ⊢ ((𝜑 → 𝜓) → (𝜓 → 𝜓))
3	1, 2	jaod 707	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))

Syntax hints:   → wi 4   ∨ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm2.62  738  pm2.73  796  pm4.72  817  undif4  3471