Theorem pm3.4 333

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 110	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	a1d 22	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107

This theorem is referenced by:  dcim  841  pclem6  1374  sbequ1  1766  sbequ8  1845  en2lp  4547