Theorem animorrl 979

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 489	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	orcd 871	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∧ wa 400   ∨ wo 845

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 210  df-an 401  df-or 846

This theorem is referenced by:  nelpr1  4551  ccatsymb  13976  sadadd2lem2  15842  mreexexlem4d  16969  drngnidl  20063  ppttop  21700  wilthlem2  25746  bcmono  25953  addsqnreup  26119  mideulem2  26620  linds2eq  31089  fnwe2lem3  40362  disjxp1  42069  nnfoctbdjlem  43453