Theorem e3bi 16606

Description: Biconditional form of e3 16605. syl8ib 234 is e3bi 16606 without virtual deductions.

Hypotheses

Ref	Expression
e3bi.1	|- . ph, ps, ch   ⊢   th .
e3bi.2	|- (th <-> ta)

Assertion

Ref	Expression
e3bi	|- . ph, ps, ch   ⊢   ta .

Proof of Theorem e3bi

Step	Hyp	Ref	Expression
1		e3bi.1	. 2 |- . ph, ps, ch   ⊢   th .
2		e3bi.2	. . 3 |- (th <-> ta)
3	2	biimpi 168	. 2 |- (th -> ta)
4	1, 3	e3 16605	1 |- . ph, ps, ch   ⊢   ta .

Syntax hints:   <-> wb 163   . vd3 16493

This theorem is referenced by:  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-3an 860  df-vd3 16494

Copyright terms: Public domain