Theorem nanbi12d 1463

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

Hypotheses

Ref	Expression
nanbid.1	|- ( ph -> ( ps <-> ch ) )
nanbi12d.2	|- ( ph -> ( th <-> ta ) )

Assertion

Ref	Expression
nanbi12d	|- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) )

Proof of Theorem nanbi12d

Step	Hyp	Ref	Expression
1		nanbid.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		nanbi12d.2	. 2 |- ( ph -> ( th <-> ta ) )
3		nanbi12 1457	. 2 |- ( ( ( ps <-> ch ) /\ ( th <-> ta ) ) -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) )
4	1, 2, 3	syl2anc 693	1 |- ( ph -> ( ( ps -/\ th ) <-> ( ch -/\ ta ) ) )

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:  rp-fakenanass  37860