Theorem 3anbi3d 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
3anbi3d	|- ( ph -> ( ( th /\ ta /\ ps ) <-> ( th /\ ta /\ ch ) ) )

Proof of Theorem 3anbi3d

Step	Hyp	Ref	Expression
1		biidd 171	. 2 |- ( ph -> ( th <-> th ) )
2		3anbi1d.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	3anbi13d 1309	1 |- ( ph -> ( ( th /\ ta /\ ps ) <-> ( th /\ ta /\ ch ) ) )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 973

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 975

This theorem is referenced by:  ceqsex3v  2772  ceqsex4v  2773  ceqsex8v  2775  vtocl3gaf  2799  mob  2912  ordsoexmid  4546  tfr1onlemaccex  6327  tfrcllemaccex  6340  fseq1m1p1  10051  summodc  11346  fsum3  11350  divalglemnn  11877  divalglemeunn  11880  divalglemex  11881  divalglemeuneg  11882