Theorem bnj1095 30852

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

Hypothesis

Ref	Expression
bnj1095.1	|- ( ph <-> A. x e. A ps )

Assertion

Ref	Expression
bnj1095	|- ( ph -> A. x ph )

Proof of Theorem bnj1095

Step	Hyp	Ref	Expression
1		bnj1095.1	. 2 |- ( ph <-> A. x e. A ps )
2		hbra1 2942	. 2 |- ( A. x e. A ps -> A. x A. x e. A ps )
3	1, 2	hbxfrbi 1752	1 |- ( ph -> A. x ph )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   A.wral 2912

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-ral 2917

This theorem is referenced by:  bnj1379  30901  bnj605  30977  bnj594  30982  bnj607  30986  bnj911  31002  bnj964  31013  bnj983  31021  bnj1093  31048  bnj1123  31054  bnj1145  31061  bnj1417  31109