Theorem animorr 976

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 483	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 872	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 394   ∨ wo 845

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 395  df-or 846

This theorem is referenced by:  nelpr2  4660  hashf1  14458  gsummoncoe1  22234  mp2pm2mplem4  22731  relogbf  26743  tgcolg  28378  colmid  28512  3vfriswmgrlem  30107  satfvsucsuc  35008  bj-dfbi6  36084  itschlc0xyqsol1  47917