Theorem nfsbc1 2781

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 2780	. 2 |- ( T. -> F/ x [. A / x ]. ph )
4	3	trud 1252	1 |- F/ x [. A / x ]. ph

Syntax hints:   T. wtru 1244   F/wnf 1349   F/_wnfc 2165   [.wsbc 2764

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765

This theorem is referenced by:  nfsbc1v  2782  riotass2  5494  riotass  5495  bj-intabssel  9928