Theorem nfcsb1 3870

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 3869	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1548	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1542  Ⅎwnfc 2881  ⦋csb 3847

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 2115  ax-9 2123  ax-10 2146  ax-11 2162  ax-12 2182  ax-ext 2705

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 2712  df-cleq 2725  df-clel 2808  df-nfc 2883  df-sbc 3739  df-csb 3848

This theorem is referenced by:  nfcsb1v  3871  fsumsplit1  15662  iundisj  25486  disjabrex  32573  disjabrexf  32574  iundisjf  32580  iundisjfi  32789  rdgssun  37433  evl1gprodd  42220  disjinfi  45303  fsumsermpt  45693  climsubmpt  45772  climeldmeqmpt  45780  climfveqmpt  45783  climfveqmpt3  45794  climeldmeqmpt3  45801  climinf2mpt  45826  climinfmpt  45827  dvmptmulf  46049  dvnmptdivc  46050  sge0lempt  46522  sge0isummpt2  46544  meadjiun  46578  hoimbl2  46777  vonhoire  46784