Theorem nfsbc1 3069

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 3068	. 2 |- ( T. -> F/ x [. A / x ]. ph )
4	3	mptru 1411	1 |- F/ x [. A / x ]. ph

This proof depends on syntax axioms:   T. wtru 1403   F/wnf 1513   F/_wnfc 2379   [.wsbc 3051

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-sbc 3052

This theorem is used by:  nfsbc1v  3070  riotass2  6067  riotass  6068  bj-intabssel  16817