Theorem animorrl 977

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 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	orcd 869	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∧ wa 395   ∨ wo 843

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 396  df-or 844

This theorem is referenced by:  nelpr1  4586  ccatsymb  14215  sadadd2lem2  16085  mreexexlem4d  17273  drngnidl  20413  ppttop  22065  wilthlem2  26123  bcmono  26330  addsqnreup  26496  mideulem2  26999  linds2eq  31477  fnwe2lem3  40793  disjxp1  42506  nnfoctbdjlem  43883