Theorem nanbi12 1297

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

Assertion

Ref	Expression
nanbi12	|- (((ph <-> ps) /\ (ch <-> th)) -> ((ph -/\ ch) <-> (ps -/\ th)))

Proof of Theorem nanbi12

Step	Hyp	Ref	Expression
1		nanbi1 1295	. 2 |- ((ph <-> ps) -> ((ph -/\ ch) <-> (ps -/\ ch)))
2		nanbi2 1296	. 2 |- ((ch <-> th) -> ((ps -/\ ch) <-> (ps -/\ th)))
3	1, 2	sylan9bb 680	1 |- (((ph <-> ps) /\ (ch <-> th)) -> ((ph -/\ ch) <-> (ps -/\ th)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358   -/\ wnan 1287

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-nan 1288

This theorem is used by:  nanbi12i  1300  nanbi12d  1303