Theorem nfsbc1 2992

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 2991	. 2 |- ( T. -> F/ x [. A / x ]. ph )
4	3	mptru 1372	1 |- F/ x [. A / x ]. ph

Syntax hints:   T. wtru 1364   F/wnf 1470   F/_wnfc 2316   [.wsbc 2974

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-sbc 2975

This theorem is referenced by:  nfsbc1v  2993  riotass2  5870  riotass  5871  bj-intabssel  14768