Theorem nanbi12i 1460

Description: Join two logical equivalences with anti-conjunction. (Contributed by SF, 2-Jan-2018.)

Hypotheses

Ref	Expression
nanbii.1	|- ( ph <-> ps )
nanbi12i.2	|- ( ch <-> th )

Assertion

Ref	Expression
nanbi12i	|- ( ( ph -/\ ch ) <-> ( ps -/\ th ) )

Proof of Theorem nanbi12i

Step	Hyp	Ref	Expression
1		nanbii.1	. 2 |- ( ph <-> ps )
2		nanbi12i.2	. 2 |- ( ch <-> th )
3		nanbi12 1457	. 2 |- ( ( ( ph <-> ps ) /\ ( ch <-> th ) ) -> ( ( ph -/\ ch ) <-> ( ps -/\ th ) ) )
4	1, 2, 3	mp2an 708	1 |- ( ( ph -/\ ch ) <-> ( ps -/\ th ) )

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: (None)