Theorem pm2.62 743

Description: Theorem *2.62 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 13-Dec-2013.)

Assertion

Ref	Expression
pm2.62	⊢ ((𝜑 ∨ 𝜓) → ((𝜑 → 𝜓) → 𝜓))

Proof of Theorem pm2.62

Step	Hyp	Ref	Expression
1		pm2.621 742	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))
2	1	com12 30	1 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 → 𝜓) → 𝜓))

Syntax hints:   → wi 4   ∨ wo 703

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 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  dfor2dc  890