Theorem nfdh 1767

Description: Deduce that x is not free in ps in a context. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
nfdh.1	|- (ph -> A.xph)
nfdh.2	|- (ph -> (ps -> A.xps))

Assertion

Ref	Expression
nfdh	|- (ph -> F/xps)

Proof of Theorem nfdh

Step	Hyp	Ref	Expression
1		nfdh.1	. . 3 |- (ph -> A.xph)
2	1	nfi 1551	. 2 |- F/xph
3		nfdh.2	. 2 |- (ph -> (ps -> A.xps))
4	2, 3	nfd 1766	1 |- (ph -> F/xps)

Syntax hints:   -> wi 4  A.wal 1540   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  hbimd  1815  ax11indalem  2197  ax11inda2ALT  2198