Theorem nfsbc1 2968

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

Hypothesis

Ref	Expression
nfsbc1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfsbc1	⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Proof of Theorem nfsbc1

Step	Hyp	Ref	Expression
1		nfsbc1.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfsbc1d 2967	. 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
4	3	mptru 1352	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  ⊤wtru 1344  Ⅎwnf 1448  Ⅎwnfc 2295  [wsbc 2951

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-sbc 2952

This theorem is referenced by:  nfsbc1v  2969  riotass2  5824  riotass  5825  bj-intabssel  13670