Theorem e2bi 16522

Description: Bi-conditional form of e2 16521. syl6ib 229 is e2bi 16522 without virtual deductions.

Hypotheses

Ref	Expression
e2bi.1	|- . ph, ps   ⊢   ch .
e2bi.2	|- (ch <-> th)

Assertion

Ref	Expression
e2bi	|- . ph, ps   ⊢   th .

Proof of Theorem e2bi

Step	Hyp	Ref	Expression
1		e2bi.1	. 2 |- . ph, ps   ⊢   ch .
2		e2bi.2	. . 3 |- (ch <-> th)
3	2	biimpi 168	. 2 |- (ch -> th)
4	1, 3	e2 16521	1 |- . ph, ps   ⊢   th .

Syntax hints:   <-> wb 163   . vd2 16488

This theorem is referenced by:  snssiALTVD 16650  eqsbc3rVD 16664  en3lplem2VD 16668

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

Copyright terms: Public domain