Theorem xornan2 1473

Description: XOR implies NAND (written with the -/\ connector). (Contributed by BJ, 19-Apr-2019.)

Assertion

Ref	Expression
xornan2	|- ( ( ph \/_ ps ) -> ( ph -/\ ps ) )

Proof of Theorem xornan2

Step	Hyp	Ref	Expression
1		xornan 1472	. 2 |- ( ( ph \/_ ps ) -> -. ( ph /\ ps ) )
2		df-nan 1448	. 2 |- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
3	1, 2	sylibr 224	1 |- ( ( ph \/_ ps ) -> ( ph -/\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   -/\ wnan 1447   \/_ wxo 1464

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-nan 1448  df-xor 1465

This theorem is referenced by: (None)