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 487	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	orcd 869	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∧ wa 398   ∨ 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 209  df-an 399  df-or 844

This theorem is referenced by:  nelpr1  4586  ccatsymb  13930  sadadd2lem2  15793  mreexexlem4d  16912  drngnidl  19996  ppttop  21609  wilthlem2  25640  bcmono  25847  addsqnreup  26013  mideulem2  26514  linds2eq  30936  fnwe2lem3  39645  disjxp1  41324  nnfoctbdjlem  42731