Theorem nfcsb1 3918

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 3917	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1549	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  ⦋csb 3894

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-sbc 3779  df-csb 3895

This theorem is referenced by:  nfcsb1v  3919  fsumsplit1  15691  iundisj  25065  disjabrex  31813  disjabrexf  31814  iundisjf  31820  iundisjfi  32007  rdgssun  36259  disjinfi  43891  fsumsermpt  44295  climsubmpt  44376  climeldmeqmpt  44384  climfveqmpt  44387  climfveqmpt3  44398  climeldmeqmpt3  44405  climinf2mpt  44430  climinfmpt  44431  dvmptmulf  44653  dvnmptdivc  44654  sge0f1o  45098  sge0lempt  45126  sge0isummpt2  45148  meadjiun  45182  hoimbl2  45381  vonhoire  45388