Theorem nanbi1i 1298

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 1295	. 2 |- ((ph <-> ps) -> ((ph -/\ ch) <-> (ps -/\ ch)))
3	1, 2	ax-mp 5	1 |- ((ph -/\ ch) <-> (ps -/\ ch))

Syntax hints:   <-> wb 176   -/\ wnan 1287

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 177  df-an 360  df-nan 1288

This theorem is referenced by: (None)