Theorem nfcsb1 3874

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

Hypothesis

Ref	Expression
nfcsb1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfcsb1	⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Proof of Theorem nfcsb1

Step	Hyp	Ref	Expression
1		nfcsb1.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfcsb1d 3873	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1577	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

This proof depends on syntax axioms:  ⊤wtru 1571  Ⅎwnfc 2911  ⦋csb 3851

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-11 2197  ax-12 2216  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-nfc 2913  df-sbc 3743  df-csb 3852

This theorem is used by:  nfcsb1v  3875  fsumsplit1  15943  iundisj  25902  disjabrex  33251  disjabrexf  33252  iundisjf  33258  iundisjfi  33461  rdgssun  38506  evl1gprodd  43370  disjinfi  46422  fsumsermpt  46806  climsubmpt  46885  climeldmeqmpt  46893  climfveqmpt  46896  climfveqmpt3  46907  climeldmeqmpt3  46914  climinf2mpt  46939  climinfmpt  46940  dvmptmulf  47162  dvnmptdivc  47163  sge0lempt  47635  sge0isummpt2  47657  meadjiun  47691  hoimbl2  47890  vonhoire  47897