Theorem hbra1 2942

Description: The setvar x is not free in A. x e. A ph. (Contributed by NM, 18-Oct-1996.) (Proof shortened by Wolf Lammen, 7-Dec-2019.)

Assertion

Ref	Expression
hbra1	|- ( A. x e. A ph -> A. x A. x e. A ph )

Proof of Theorem hbra1

Step	Hyp	Ref	Expression
1		nfra1 2941	. 2 |- F/ x A. x e. A ph
2	1	nf5ri 2065	1 |- ( A. x e. A ph -> A. x A. x e. A ph )

Syntax hints:   -> wi 4   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:  bnj1095  30852  bnj1309  31090  mpt2bi123f  33971  hbra2VD  39096  tratrbVD  39097  ssralv2VD  39102