Theorem bnj1276 30885

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

Hypotheses

Ref	Expression
bnj1276.1	|- ( ph -> A. x ph )
bnj1276.2	|- ( ps -> A. x ps )
bnj1276.3	|- ( ch -> A. x ch )
bnj1276.4	|- ( th <-> ( ph /\ ps /\ ch ) )

Assertion

Ref	Expression
bnj1276	|- ( th -> A. x th )

Proof of Theorem bnj1276

Step	Hyp	Ref	Expression
1		bnj1276.4	. 2 |- ( th <-> ( ph /\ ps /\ ch ) )
2		bnj1276.1	. . 3 |- ( ph -> A. x ph )
3		bnj1276.2	. . 3 |- ( ps -> A. x ps )
4		bnj1276.3	. . 3 |- ( ch -> A. x ch )
5	2, 3, 4	hb3an 2129	. 2 |- ( ( ph /\ ps /\ ch ) -> A. x ( ph /\ ps /\ ch ) )
6	1, 5	hbxfrbi 1752	1 |- ( th -> A. x th )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037   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  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-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)