Theorem bj-nfs1t 31255

Description: A theorem close to a closed form of nfs1 2155. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-nfs1t	|- ( A. x ( ph -> A. y ph ) -> F/ x [ y / x ] ph )

Proof of Theorem bj-nfs1t

Step	Hyp	Ref	Expression
1		bj-hbsb3t 31253	. . 3 |- ( A. x ( ph -> A. y ph ) -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )
2	1	axc4i 1952	. 2 |- ( A. x ( ph -> A. y ph ) -> A. x ( [ y / x ] ph -> A. x [ y / x ] ph ) )
3		df-nf 1664	. 2 |- ( F/ x [ y / x ] ph <-> A. x ( [ y / x ] ph -> A. x [ y / x ] ph ) )
4	2, 3	sylibr 215	1 |- ( A. x ( ph -> A. y ph ) -> F/ x [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1435   F/wnf 1663   [wsb 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-12 1904  ax-13 2052

This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1787

This theorem is referenced by:  bj-nfs1t2  31256