Theorem bnj1198 30866

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj1198.1	|- ( ph -> E. x ps )
bnj1198.2	|- ( ps' <-> ps )

Assertion

Ref	Expression
bnj1198	|- ( ph -> E. x ps' )

Proof of Theorem bnj1198

Step	Hyp	Ref	Expression
1		bnj1198.1	. 2 |- ( ph -> E. x ps )
2		bnj1198.2	. . 3 |- ( ps' <-> ps )
3	2	exbii 1774	. 2 |- ( E. x ps' <-> E. x ps )
4	1, 3	sylibr 224	1 |- ( ph -> E. x ps' )

Syntax hints:   -> wi 4   <-> wb 196   E.wex 1704

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  df-ex 1705

This theorem is referenced by:  bnj1209  30867  bnj1275  30884  bnj1340  30894  bnj1345  30895  bnj605  30977  bnj607  30986  bnj906  31000  bnj908  31001  bnj1189  31077  bnj1450  31118  bnj1312  31126