Theorem pm3.4 544

Description: Conjunction implies implication. Theorem *3.4 of [WhiteheadRussell] p. 113. (Contributed by NM, 31-Jul-1995.)

Assertion

Ref	Expression
pm3.4	⊢ ((φ ∧ ψ) → (φ → ψ))

Proof of Theorem pm3.4

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((φ ∧ ψ) → ψ)
2	1	a1d 22	1 ⊢ ((φ ∧ ψ) → (φ → 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:  sbequ1  1918