Theorem animorrl 838

Description: Conjunction implies disjunction with one common formula (4/4). (Contributed by BJ, 4-Oct-2019.)

Assertion

Ref	Expression
animorrl	⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

Proof of Theorem animorrl

Step	Hyp	Ref	Expression
1		simpr 110	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	orcd 745	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  zzlesq  11160  ccatsymb  11385  nnwosdc  12834  chtprm  16183  efchtqdvds  16187  ppidif  16191  prmorcht  16204  ppiqub  16215  bcmono  16226  wexmiddiffi  17166