Theorem ornld 940

Description: Selecting one statement from a disjunction if one of the disjuncted statements is false. (Contributed by AV, 6-Sep-2018.) (Proof shortened by AV, 13-Oct-2018.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)

Assertion

Ref	Expression
ornld	|- ( ph -> ( ( ( ph -> ( th \/ ta ) ) /\ -. th ) -> ta ) )

Proof of Theorem ornld

Step	Hyp	Ref	Expression
1		pm3.35 611	. . 3 |- ( ( ph /\ ( ph -> ( th \/ ta ) ) ) -> ( th \/ ta ) )
2	1	ord 392	. 2 |- ( ( ph /\ ( ph -> ( th \/ ta ) ) ) -> ( -. th -> ta ) )
3	2	expimpd 629	1 |- ( ph -> ( ( ( ph -> ( th \/ ta ) ) /\ -. th ) -> ta ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384

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  df-an 386

This theorem is referenced by:  friendshipgt3  27256  ralralimp  41295