Theorem wl-nfalv 33312

Description: If x is not present in ph, it is not free in A. y ph. (Contributed by Wolf Lammen, 11-Jan-2020.)

Assertion

Ref	Expression
wl-nfalv	|- F/ x A. y ph

Distinct variable group:   ph, x

Allowed substitution hint:   ph( y)

Proof of Theorem wl-nfalv

Step	Hyp	Ref	Expression
1		ax-5 1839	. . 3 |- ( ph -> A. x ph )
2	1	hbal 2036	. 2 |- ( A. y ph -> A. x A. y ph )
3	2	nf5i 2024	1 |- F/ x A. y ph

Syntax hints:   A.wal 1481   F/wnf 1708

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-10 2019  ax-11 2034

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)