Theorem animorlr 977

Description: Conjunction implies disjunction with one common formula (3/4). (Contributed by BJ, 4-Oct-2019.)

Assertion

Ref	Expression
animorlr	⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜑))

Proof of Theorem animorlr

Step	Hyp	Ref	Expression
1		simpl 483	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	olcd 871	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜑))

Syntax hints:   → wi 4   ∧ wa 396   ∨ wo 844

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  df-or 845

This theorem is referenced by:  sumhash  16597