Theorem pm3.4 582

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 476	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	a1d 25	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓))

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  cases2  1005  sbequ1  2096  bj-sbsb  32012  jabtaib  39748  confun4  39758  plvcofphax  39763  afvres  39901