Theorem 3anbi1d 897

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

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

This theorem is referenced by:  abfii4OLD 4564  mulcantOLD 5691  hausnei 7784  isgrp2i 8076  nvcni 8329  nvcni2 8330  fiv 10482  fivOLD 10483  rcfpfil 10597  rcfpfilOLD 10598

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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