Theorem ts3an3 33959

Description: A Tseitin axiom for triple logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018.)

Assertion

Ref	Expression
ts3an3	|- ( th -> ( ch \/ -. ( ph /\ ps /\ ch ) ) )

Proof of Theorem ts3an3

Step	Hyp	Ref	Expression
1		tsan3 33950	. 2 |- ( th -> ( ch \/ -. ( ( ph /\ ps ) /\ ch ) ) )
2		df-3an 1039	. . . 4 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
3	2	notbii 310	. . 3 |- ( -. ( ph /\ ps /\ ch ) <-> -. ( ( ph /\ ps ) /\ ch ) )
4	3	orbi2i 541	. 2 |- ( ( ch \/ -. ( ph /\ ps /\ ch ) ) <-> ( ch \/ -. ( ( ph /\ ps ) /\ ch ) ) )
5	1, 4	sylibr 224	1 |- ( th -> ( ch \/ -. ( ph /\ ps /\ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384   /\ w3a 1037

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  df-3an 1039

This theorem is referenced by: (None)