Theorem animorl 979

Description: Conjunction implies disjunction with one common formula (1/4). (Contributed by BJ, 4-Oct-2019.)

Assertion

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

Proof of Theorem animorl

Step	Hyp	Ref	Expression
1		simpl 482	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	orcd 873	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ∨ 𝜒))

Syntax hints:   → wi 4   ∧ wa 395   ∨ wo 847

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 207  df-an 396  df-or 848

This theorem is referenced by:  cadan  1609  rankxplim3  9852  wl-df2-3mintru2  37470  wl-df3-3mintru2  37471  lindslinindsimp1  48375