Theorem pm3.42 493

Description: Theorem *3.42 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.42	⊢ ((𝜓 → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem pm3.42

Step	Hyp	Ref	Expression
1		simpr 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	imim1i 63	1 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))

Syntax hints:   → wi 4   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  bnj1101  32664  islinindfis  45678