Theorem nfcsb1 3861

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 3860	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1549	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  ⦋csb 3838

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-sbc 3730  df-csb 3839

This theorem is referenced by:  nfcsb1v  3862  fsumsplit1  15696  iundisj  25524  disjabrex  32672  disjabrexf  32673  iundisjf  32679  iundisjfi  32889  rdgssun  37705  evl1gprodd  42567  disjinfi  45637  fsumsermpt  46024  climsubmpt  46103  climeldmeqmpt  46111  climfveqmpt  46114  climfveqmpt3  46125  climeldmeqmpt3  46132  climinf2mpt  46157  climinfmpt  46158  dvmptmulf  46380  dvnmptdivc  46381  sge0lempt  46853  sge0isummpt2  46875  meadjiun  46909  hoimbl2  47108  vonhoire  47115