Theorem tsan3 33950

Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)

Assertion

Ref	Expression
tsan3	|- ( th -> ( ps \/ -. ( ph /\ ps ) ) )

Proof of Theorem tsan3

Step	Hyp	Ref	Expression
1		pm3.14 523	. . . 4 |- ( ( -. ph \/ -. ps ) -> -. ( ph /\ ps ) )
2	1	olcs 410	. . 3 |- ( -. ps -> -. ( ph /\ ps ) )
3	2	orri 391	. 2 |- ( ps \/ -. ( ph /\ ps ) )
4	3	a1i 11	1 |- ( th -> ( ps \/ -. ( ph /\ ps ) ) )

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:  tsna3  33953  ts3an3  33959  mpt2bi123f  33971  mptbi12f  33975