Theorem bj-jaoi1 37196

Description: Shortens orfa2 38769 (58>53), pm1.2 917 (20>18), pm1.2 917 (20>18), pm2.4 920 (31>25), pm2.41 921 (31>25), pm2.42 957 (38>32), pm3.2ni 894 (43>39), pm4.44 1012 (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 23	. 2 ⊢ (𝜓 → 𝜓)
3	1, 2	jaoi 871	1 ⊢ ((𝜑 ∨ 𝜓) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  bj-falor2  37210  bj-prmoore  37789