Theorem animorr 994

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 490	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 888	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by:  nelpr2  4610  hashf1  14609  gsummoncoe1  22635  mp2pm2mplem4  23136  relogbf  27128  tgcolg  29026  colmid  29169  3vfriswmgrlem  30887  satfvsucsuc  36220  bj-dfbi6  37541  itschlc0xyqsol1  49986