Theorem nanbi2 1456

Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)

Assertion

Ref	Expression
nanbi2	|- ( ( ph <-> ps ) -> ( ( ch -/\ ph ) <-> ( ch -/\ ps ) ) )

Proof of Theorem nanbi2

Step	Hyp	Ref	Expression
1		nanbi1 1455	. 2 |- ( ( ph <-> ps ) -> ( ( ph -/\ ch ) <-> ( ps -/\ ch ) ) )
2		nancom 1450	. 2 |- ( ( ch -/\ ph ) <-> ( ph -/\ ch ) )
3		nancom 1450	. 2 |- ( ( ch -/\ ps ) <-> ( ps -/\ ch ) )
4	1, 2, 3	3bitr4g 303	1 |- ( ( ph <-> ps ) -> ( ( ch -/\ ph ) <-> ( ch -/\ ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   -/\ wnan 1447

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-an 386  df-nan 1448

This theorem is referenced by:  nanbi12  1457  nanbi2i  1459  nanbi2d  1462  nabi2  32390  rp-fakenanass  37860