Theorem nfsbc1 3454

Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993.) (Revised 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 11	. . 3 |- ( T. -> F/_ x A )
3	2	nfsbc1d 3453	. 2 |- ( T. -> F/ x [. A / x ]. ph )
4	3	trud 1493	1 |- F/ x [. A / x ]. ph

Syntax hints:   T. wtru 1484   F/wnf 1708   F/_wnfc 2751   [.wsbc 3435

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-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-sbc 3436

This theorem is referenced by:  nfsbc1v  3455  riotass2  6638  riotass  6639  uzwo4  39221