Theorem nanbi12d 1303

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 1297	. 2 |- (((ps <-> ch) /\ (th <-> ta)) -> ((ps -/\ th) <-> (ch -/\ ta)))
4	1, 2, 3	syl2anc 642	1 |- (ph -> ((ps -/\ th) <-> (ch -/\ ta)))

Syntax hints:   -> wi 4   <-> 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:  ninjust  3211  elning  3218  elun  3221