Theorem bj-nfs1 32716

Description: Shorter proof of nfs1 2365 (three essential steps instead of four). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-nfs1.nf	|- F/ y ph

Assertion

Ref	Expression
bj-nfs1	|- F/ x [ y / x ] ph

Proof of Theorem bj-nfs1

Step	Hyp	Ref	Expression
1		bj-nfs1t2 32715	. 2 |- ( A. x F/ y ph -> F/ x [ y / x ] ph )
2		bj-nfs1.nf	. 2 |- F/ y ph
3	1, 2	mpg 1724	1 |- F/ x [ y / x ] ph

Syntax hints:   F/wnf 1708   [wsb 1880

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  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)