Theorem nfcsb1 3868

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 3867	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1548	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1542  Ⅎwnfc 2879  ⦋csb 3845

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-10 2144  ax-11 2160  ax-12 2180  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-nf 1785  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-nfc 2881  df-sbc 3737  df-csb 3846

This theorem is referenced by:  nfcsb1v  3869  fsumsplit1  15658  iundisj  25482  disjabrex  32569  disjabrexf  32570  iundisjf  32576  iundisjfi  32785  rdgssun  37429  evl1gprodd  42216  disjinfi  45294  fsumsermpt  45684  climsubmpt  45763  climeldmeqmpt  45771  climfveqmpt  45774  climfveqmpt3  45785  climeldmeqmpt3  45792  climinf2mpt  45817  climinfmpt  45818  dvmptmulf  46040  dvnmptdivc  46041  sge0lempt  46513  sge0isummpt2  46535  meadjiun  46569  hoimbl2  46768  vonhoire  46775