Theorem 3anbi2d 898

Description: Deduction adding conjuncts to an equivalence.

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		pm4.2d 171	. 2 |- (ph -> (th <-> th))
2		3anbi1d.1	. 2 |- (ph -> (ps <-> ch))
3	1, 2	3anbi12d 894	1 |- (ph -> ((th /\ ps /\ ta) <-> (th /\ ch /\ ta)))

Syntax hints:   -> wi 3   <-> wb 146   /\ w3a 775

This theorem is referenced by:  acdc3 7487  acdc5 7493  hausnei 7784  isgrp2i 8076  isnvlem 8229  nvi 8233  csmdsym 10261  isalg 10653  algi 10660

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 777

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