Theorem pm3.35 339

Description: Conjunctive detachment. Theorem *3.35 of [WhiteheadRussell] p. 112. (Contributed by NM, 14-Dec-2002.)

Assertion

Ref	Expression
pm3.35	⊢ ((𝜑 ∧ (𝜑 → 𝜓)) → 𝜓)

Proof of Theorem pm3.35

Step	Hyp	Ref	Expression
1		pm2.27 39	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
2	1	imp 122	1 ⊢ ((𝜑 ∧ (𝜑 → 𝜓)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem is referenced by:  xordc1  1324  19.35-1  1555  ax9o  1628  sbequ8  1768  r19.29af2  2496  r19.29vva  2500  r19.35-1  2504  intab  3665