Theorem bj-jaoi2 32557

Description: Shortens consensus 999 (110>106), elnn0z 11390 (336>329), pm1.2 535 (20>19), pm3.2ni 899 (43>39), pm4.44 601 (55>51). (Contributed by BJ, 30-Sep-2019.)

Hypothesis

Ref	Expression
bj-jaoi1.1	|- ( ph -> ps )

Assertion

Ref	Expression
bj-jaoi2	|- ( ( ps \/ ph ) -> ps )

Proof of Theorem bj-jaoi2

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ps -> ps )
2		bj-jaoi1.1	. 2 |- ( ph -> ps )
3	1, 2	jaoi 394	1 |- ( ( ps \/ ph ) -> ps )

Syntax hints:   -> wi 4   \/ wo 383

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 197  df-or 385

This theorem is referenced by:  bj-consensus  32562