Theorem ax5ea 1842

Description: If a formula holds for some value of a variable not occurring in it, then it holds for all values of that variable. (Contributed by BJ, 28-Dec-2020.)

Assertion

Ref	Expression
ax5ea	|- ( E. x ph -> A. x ph )

Distinct variable group:   ph, x

Proof of Theorem ax5ea

Step	Hyp	Ref	Expression
1		ax5e 1841	. 2 |- ( E. x ph -> ph )
2		ax-5 1839	. 2 |- ( ph -> A. x ph )
3	1, 2	syl 17	1 |- ( E. x ph -> A. x ph )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  nfv  1843