Theorem selconj 33902

Description: An inference for selecting one of a list of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019.)

Hypothesis

Ref	Expression
selconj.1	|- ( ph <-> ( ps /\ ch ) )

Assertion

Ref	Expression
selconj	|- ( ( et /\ ph ) <-> ( ps /\ ( et /\ ch ) ) )

Proof of Theorem selconj

Step	Hyp	Ref	Expression
1		selconj.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2	1	anbi2i 730	. 2 |- ( ( et /\ ph ) <-> ( et /\ ( ps /\ ch ) ) )
3		an12 838	. 2 |- ( ( ps /\ ( et /\ ch ) ) <-> ( et /\ ( ps /\ ch ) ) )
4	2, 3	bitr4i 267	1 |- ( ( et /\ ph ) <-> ( ps /\ ( et /\ ch ) ) )

Syntax hints:   <-> wb 196   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)