Theorem e2bir 16523

Description: Right bi-conditional form of e2 16521. syl6ibr 230 is e2bir 16523 without virtual deductions.

Hypotheses

Ref	Expression
e2bir.1	|- . ph, ps   ⊢   ch .
e2bir.2	|- (th <-> ch)

Assertion

Ref	Expression
e2bir	|- . ph, ps   ⊢   th .

Proof of Theorem e2bir

Step	Hyp	Ref	Expression
1		e2bir.1	. 2 |- . ph, ps   ⊢   ch .
2		e2bir.2	. . 3 |- (th <-> ch)
3	2	biimpri 169	. 2 |- (ch -> th)
4	1, 3	e2 16521	1 |- . ph, ps   ⊢   th .

Syntax hints:   <-> wb 163   . vd2 16488

This theorem is referenced by:  trsspwALT 16640  pwtrVD 16646  eqsbc3rVD 16664  tpid3gVD 16666

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 164  df-an 242  df-vd2 16489

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