Theorem e1bi 16519

Description: Biconditional form of e1_ 16518. sylib 215 is e1bi 16519 without virtual deductions.

Hypotheses

Ref	Expression
e1bi.1	|- . ph   ⊢   ps .
e1bi.2	|- (ps <-> ch)

Assertion

Ref	Expression
e1bi	|- . ph   ⊢   ch .

Proof of Theorem e1bi

Step	Hyp	Ref	Expression
1		e1bi.1	. 2 |- . ph   ⊢   ps .
2		e1bi.2	. . 3 |- (ps <-> ch)
3	2	biimpi 168	. 2 |- (ps -> ch)
4	1, 3	e1_ 16518	1 |- . ph   ⊢   ch .

Syntax hints:   <-> wb 163   . vd1 16479

This theorem is referenced by:  zfregs2VD 16665  tpid3gVD 16666  en3lplem2VD 16668  ordelordaxrVD 16691

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-vd1 16480

Copyright terms: Public domain