Theorem nfbii2 33967

Description: Equality deduction for not-freeness. (Contributed by Giovanni Mascellani, 10-Apr-2018.)

Assertion

Ref	Expression
nfbii2	|- ( A. x ( ph <-> ps ) -> ( F/ x ph <-> F/ x ps ) )

Proof of Theorem nfbii2

Step	Hyp	Ref	Expression
1		nfa1 2028	. 2 |- F/ x A. x ( ph <-> ps )
2		sp 2053	. 2 |- ( A. x ( ph <-> ps ) -> ( ph <-> ps ) )
3	1, 2	nfbidf 2092	1 |- ( A. x ( ph <-> ps ) -> ( F/ x ph <-> F/ x ps ) )

Syntax hints:   -> wi 4   <-> wb 196   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-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

This theorem is referenced by: (None)