Theorem pm3.35 570

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 35	. 2 ⊢ (φ → ((φ → ψ) → ψ))
2	1	imp 418	1 ⊢ ((φ ∧ (φ → ψ)) → ψ)

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  2reu5  3045  intab  3957  fnfrec  6321