Theorem nanbi1i 1458

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

Hypothesis

Ref	Expression
nanbii.1	|- ( ph <-> ps )

Assertion

Ref	Expression
nanbi1i	|- ( ( ph -/\ ch ) <-> ( ps -/\ ch ) )

Proof of Theorem nanbi1i

Step	Hyp	Ref	Expression
1		nanbii.1	. 2 |- ( ph <-> ps )
2		nanbi1 1455	. 2 |- ( ( ph <-> ps ) -> ( ( ph -/\ ch ) <-> ( ps -/\ ch ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -/\ ch ) <-> ( ps -/\ ch ) )

Syntax hints:   <-> 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:  nabi1i  32391