Theorem pm3.4 822

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 490	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	a1d 26	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  cases2ALT  1064  dfss2  3924  bj-animbi  37184  bj-sbsb  37505  jabtaib  47702  confun4  47712  plvcofphax  47717  afvres  47942