Theorem tsim3 33939

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

Assertion

Ref	Expression
tsim3	|- ( th -> ( -. ps \/ ( ph -> ps ) ) )

Proof of Theorem tsim3

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- ( ps -> ( ph -> ps ) )
2	1	imori 429	. 2 |- ( -. ps \/ ( ph -> ps ) )
3	2	a1i 11	1 |- ( th -> ( -. ps \/ ( ph -> ps ) ) )

Syntax hints:   -. wn 3   -> 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:  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980