Theorem 3anbi1d 894

Description: Deduction adding conjuncts to an equivalence.

Hypothesis

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

Assertion

Ref	Expression
3anbi1d	|- (ph -> ((ps /\ th /\ ta) <-> (ch /\ th /\ ta)))

Proof of Theorem 3anbi1d

Step	Hyp	Ref	Expression
1		3anbi1d.1	. 2 |- (ph -> (ps <-> ch))
2		pm4.2i 171	. 2 |- (ph -> (th <-> th))
3	1, 2	3anbi12d 891	1 |- (ph -> ((ps /\ th /\ ta) <-> (ch /\ th /\ ta)))

Syntax hints:   -> wi 3   <-> wb 146   /\ w3a 773

This theorem is referenced by:  abfii4 4538  mulcant 5661  hausnei 7723  isgrp2i 8011  nvcni 8266  fiv 10374

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 775

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