Theorem 3anbi3d 1254

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 170	. 2 |- ( ph -> ( th <-> th ) )
2		3anbi1d.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	3anbi13d 1250	1 |- ( ph -> ( ( th /\ ta /\ ps ) <-> ( th /\ ta /\ ch ) ) )

Syntax hints:   -> wi 4   <-> wb 103   /\ w3a 924

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 926

This theorem is referenced by:  ceqsex3v  2661  ceqsex4v  2662  ceqsex8v  2664  vtocl3gaf  2688  mob  2797  ordsoexmid  4378  tfr1onlemaccex  6113  tfrcllemaccex  6126  fseq1m1p1  9509  isummo  10773  fisum  10778  divalglemnn  11196  divalglemeunn  11199  divalglemex  11200  divalglemeuneg  11201