Theorem twonotinotbothi 41101

Description: From these two negated implications it is not the case their non negated forms are both true. (Contributed by Jarvin Udandy, 11-Sep-2020.)

Hypotheses

Ref	Expression
twonotinotbothi.1	|- -. ( ph -> ps )
twonotinotbothi.2	|- -. ( ch -> th )

Assertion

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

Proof of Theorem twonotinotbothi

Step	Hyp	Ref	Expression
1		twonotinotbothi.1	. . 3 |- -. ( ph -> ps )
2	1	orci 405	. 2 |- ( -. ( ph -> ps ) \/ -. ( ch -> th ) )
3		pm3.14 523	. 2 |- ( ( -. ( ph -> ps ) \/ -. ( ch -> th ) ) -> -. ( ( ph -> ps ) /\ ( ch -> th ) ) )
4	2, 3	ax-mp 5	1 |- -. ( ( ph -> ps ) /\ ( ch -> th ) )

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: (None)