Theorem bj-jaoi1 34679

Description: Shortens orfa2 36171 (58>53), pm1.2 900 (20>18), pm1.2 900 (20>18), pm2.4 903 (31>25), pm2.41 904 (31>25), pm2.42 939 (38>32), pm3.2ni 877 (43>39), pm4.44 993 (55>51). (Contributed by BJ, 30-Sep-2019.)

Hypothesis

Ref	Expression
bj-jaoi1.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bj-jaoi1	⊢ ((𝜑 ∨ 𝜓) → 𝜓)

Proof of Theorem bj-jaoi1

Step	Hyp	Ref	Expression
1		bj-jaoi1.1	. 2 ⊢ (𝜑 → 𝜓)
2		id 22	. 2 ⊢ (𝜓 → 𝜓)
3	1, 2	jaoi 853	1 ⊢ ((𝜑 ∨ 𝜓) → 𝜓)

Syntax hints:   → wi 4   ∨ 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 206  df-or 844

This theorem is referenced by:  bj-falor2  34694  bj-prmoore  35213