Theorem animorrl 978

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 485	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	orcd 870	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∧ wa 396   ∨ wo 844

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 397  df-or 845

This theorem is referenced by:  nelpr1  4589  ccatsymb  14287  sadadd2lem2  16157  mreexexlem4d  17356  drngnidl  20500  ppttop  22157  wilthlem2  26218  bcmono  26425  addsqnreup  26591  mideulem2  27095  linds2eq  31575  fnwe2lem3  40877  fzuntgd  41065  disjxp1  42617  nnfoctbdjlem  43993