Theorem bnj1095 32130

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 2811	. 2 |- ( A. x e. A ps -> A. x A. x e. A ps )
3	1, 2	hbxfrbi 1614	1 |- ( ph -> A. x ph )

Syntax hints:   -> wi 4   <-> wb 184   A.wal 1368   A.wral 2799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794

This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591  df-ral 2804

This theorem is referenced by:  bnj1379  32179  bnj605  32255  bnj594  32260  bnj607  32264  bnj911  32280  bnj964  32291  bnj983  32299  bnj1093  32326  bnj1123  32332  bnj1145  32339  bnj1417  32387