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 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 871	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 399   ∨ 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 210  df-an 400  df-or 845

This theorem is referenced by:  nelpr2  4552  hashf1  13811  gsummoncoe1  20933  mp2pm2mplem4  21414  relogbf  25377  tgcolg  26348  colmid  26482  3vfriswmgrlem  28062  satfvsucsuc  32725  bj-dfbi6  34021  itschlc0xyqsol1  45180