Theorem wl-nanbi2 33301

Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.) (Revised by Wolf Lammen, 27-Jun-2020.)

Assertion

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

Proof of Theorem wl-nanbi2

Step	Hyp	Ref	Expression
1		imbi1 337	. 2 |- ( ( ph <-> ps ) -> ( ( ph -> -. ch ) <-> ( ps -> -. ch ) ) )
2		wl-dfnan2 33296	. 2 |- ( ( ph -/\ ch ) <-> ( ph -> -. ch ) )
3		wl-dfnan2 33296	. 2 |- ( ( ps -/\ ch ) <-> ( ps -> -. ch ) )
4	1, 2, 3	3bitr4g 303	1 |- ( ( ph <-> ps ) -> ( ( ph -/\ ch ) <-> ( ps -/\ ch ) ) )

Syntax hints:   -. wn 3   -> 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: (None)