Theorem animorlr 995

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 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	olcd 888	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜑))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∨ wo 861

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  df-or 862

This theorem is used by:  sumhash  16978