Theorem nfcsb1 3873

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 3872	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1549	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  ⦋csb 3850

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 3742  df-csb 3851

This theorem is referenced by:  nfcsb1v  3874  fsumsplit1  15672  iundisj  25509  disjabrex  32639  disjabrexf  32640  iundisjf  32646  iundisjfi  32857  rdgssun  37554  evl1gprodd  42408  disjinfi  45472  fsumsermpt  45861  climsubmpt  45940  climeldmeqmpt  45948  climfveqmpt  45951  climfveqmpt3  45962  climeldmeqmpt3  45969  climinf2mpt  45994  climinfmpt  45995  dvmptmulf  46217  dvnmptdivc  46218  sge0lempt  46690  sge0isummpt2  46712  meadjiun  46746  hoimbl2  46945  vonhoire  46952