Theorem nfsbc1 3049

Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)

Hypothesis

Ref	Expression
nfsbc1.1	|- F/_ x A

Assertion

Ref	Expression
nfsbc1	|- F/ x [. A / x ]. ph

Proof of Theorem nfsbc1

Step	Hyp	Ref	Expression
1		nfsbc1.1	. . . 4 |- F/_ x A
2	1	a1i 9	. . 3 |- ( T. -> F/_ x A )
3	2	nfsbc1d 3048	. 2 |- ( T. -> F/ x [. A / x ]. ph )
4	3	mptru 1406	1 |- F/ x [. A / x ]. ph

Syntax hints:   T. wtru 1398   F/wnf 1508   F/_wnfc 2361   [.wsbc 3031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-sbc 3032

This theorem is referenced by:  nfsbc1v  3050  riotass2  5999  riotass  6000  bj-intabssel  16385