Theorem animorr 979

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 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 873	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 395   ∨ wo 846

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 207  df-an 396  df-or 847

This theorem is referenced by:  nelpr2  4675  hashf1  14506  gsummoncoe1  22333  mp2pm2mplem4  22836  relogbf  26852  tgcolg  28580  colmid  28714  3vfriswmgrlem  30309  satfvsucsuc  35333  bj-dfbi6  36541  itschlc0xyqsol1  48500