Theorem animorr 814

Description: Conjunction implies disjunction with one common formula (2/4). (Contributed by BJ, 4-Oct-2019.)

Assertion

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

Proof of Theorem animorr

Step	Hyp	Ref	Expression
1		simpr 109	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	olcd 724	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓))

Syntax hints:   → wi 4   ∧ wa 103   ∨ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)