Theorem bj-jaoi1 36547

Description: Shortens orfa2 38068 (58>53), pm1.2 903 (20>18), pm1.2 903 (20>18), pm2.4 906 (31>25), pm2.41 907 (31>25), pm2.42 944 (38>32), pm3.2ni 880 (43>39), pm4.44 998 (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 857	1 ⊢ ((𝜑 ∨ 𝜓) → 𝜓)

Syntax hints:   → wi 4   ∨ 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-or 848

This theorem is referenced by:  bj-falor2  36561  bj-prmoore  37091