Theorem animorr 975

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 487	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 870	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 398   ∨ wo 843

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 209  df-an 399  df-or 844

This theorem is referenced by:  nelpr2  4594  hashf1  13818  gsummoncoe1  20474  mp2pm2mplem4  21419  relogbf  25371  tgcolg  26342  colmid  26476  3vfriswmgrlem  28058  satfvsucsuc  32614  bj-dfbi6  33910  itschlc0xyqsol1  44760