Theorem hbxfrbi 1752

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfreq 2730 for equality version. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypotheses

Ref	Expression
hbxfrbi.1	|- ( ph <-> ps )
hbxfrbi.2	|- ( ps -> A. x ps )

Assertion

Ref	Expression
hbxfrbi	|- ( ph -> A. x ph )

Proof of Theorem hbxfrbi

Step	Hyp	Ref	Expression
1		hbxfrbi.2	. 2 |- ( ps -> A. x ps )
2		hbxfrbi.1	. 2 |- ( ph <-> ps )
3	2	albii 1747	. 2 |- ( A. x ph <-> A. x ps )
4	1, 2, 3	3imtr4i 281	1 |- ( ph -> A. x ph )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  hbn1fw  1972  hbe1w  1976  hbe1  2021  hbexOLD  2152  hbab1  2611  hbab  2613  hbxfreq  2730  hbral  2943  bnj982  30849  bnj1095  30852  bnj1096  30853  bnj1276  30885  bnj594  30982  bnj1445  31112  bj-hbab1  32771  hbra2VD  39096