Theorem 3anbi2d 1313

Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)

Hypothesis

Ref	Expression
3anbi1d.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
3anbi2d	|- ( ph -> ( ( th /\ ps /\ ta ) <-> ( th /\ ch /\ ta ) ) )

Proof of Theorem 3anbi2d

Step	Hyp	Ref	Expression
1		biidd 171	. 2 |- ( ph -> ( th <-> th ) )
2		3anbi1d.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	3anbi12d 1309	1 |- ( ph -> ( ( th /\ ps /\ ta ) <-> ( th /\ ch /\ ta ) ) )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 974

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 976

This theorem is referenced by:  vtocl3gaf  2800  ordsoexmid  4547  ereq2  6525  genpelxp  7477  seq3f1olemp  10462  qexpclz  10501  mhmlem  12829