Theorem hbe1a 2003

Description: Dual statement of hbe1 1475. (Contributed by Wolf Lammen, 15-Sep-2021.)

Assertion

Ref	Expression
hbe1a	|- ( E. x A. x ph -> A. x ph )

Proof of Theorem hbe1a

Step	Hyp	Ref	Expression
1		nfa1 1521	. . 3 |- F/ x A. x ph
2		nf3 1649	. . 3 |- ( F/ x A. x ph <-> A. x ( E. x A. x ph -> A. x ph ) )
3	1, 2	mpbi 144	. 2 |- A. x ( E. x A. x ph -> A. x ph )
4	3	spi 1516	1 |- ( E. x A. x ph -> A. x ph )

Syntax hints:   -> wi 4   A.wal 1333   F/wnf 1440   E.wex 1472

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1441

This theorem is referenced by:  nf5-1  2004