Theorem pm3.41 498

Description: Theorem *3.41 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.41	⊢ ((𝜑 → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem pm3.41

Step	Hyp	Ref	Expression
1		simpl 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	imim1i 64	1 ⊢ ((𝜑 → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))

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:  rexss  4012  opabbrex  7472  pibt1  38119