Theorem bj-jaoi2 36574

Description: Shortens consensus 1052 (110>106), elnn0z 12628 (336>329), pm1.2 903 (20>19), 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-jaoi2	⊢ ((𝜓 ∨ 𝜑) → 𝜓)

Proof of Theorem bj-jaoi2

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜓 → 𝜓)
2		bj-jaoi1.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	jaoi 857	1 ⊢ ((𝜓 ∨ 𝜑) → 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-consensus  36580