Theorem pm4.42r 973

Description: One direction of Theorem *4.42 of [WhiteheadRussell] p. 119. (Contributed by Jim Kingdon, 4-Aug-2018.)

Assertion

Ref	Expression
pm4.42r	⊢ (((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓)) → 𝜑)

Proof of Theorem pm4.42r

Step	Hyp	Ref	Expression
1		simpl 109	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2		simpl 109	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜑)
3	1, 2	jaoi 717	1 ⊢ (((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓)) → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 104   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)