Theorem pm5.3 573

Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm5.3	⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜒)))

Proof of Theorem pm5.3

Step	Hyp	Ref	Expression
1		simpl 483	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	biantrurd 533	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ↔ (𝜑 ∧ 𝜒)))
3	2	pm5.74i 270	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜒)))

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 396

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 397

This theorem is referenced by:  cusgr3cyclex  33098  clss2lem  41219