Theorem animorr 1002

Description: Conjunction implies disjunction with one common formula (2/4). (Contributed by BJ, 4-Oct-2019.)

Assertion

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

Proof of Theorem animorr

Step	Hyp	Ref	Expression
1		simpr 478	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 901	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 385   ∨ wo 874

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 199  df-an 386  df-or 875

This theorem is referenced by:  gsummoncoe1  19996  3vfriswmgrlem  27626  bj-dfbi6  33064  nelpr2  40020