Theorem nfcsb1 3874

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 3873	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1549	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  ⦋csb 3851

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 3743  df-csb 3852

This theorem is referenced by:  nfcsb1v  3875  fsumsplit1  15680  iundisj  25517  disjabrex  32668  disjabrexf  32669  iundisjf  32675  iundisjfi  32886  rdgssun  37622  evl1gprodd  42476  disjinfi  45540  fsumsermpt  45928  climsubmpt  46007  climeldmeqmpt  46015  climfveqmpt  46018  climfveqmpt3  46029  climeldmeqmpt3  46036  climinf2mpt  46061  climinfmpt  46062  dvmptmulf  46284  dvnmptdivc  46285  sge0lempt  46757  sge0isummpt2  46779  meadjiun  46813  hoimbl2  47012  vonhoire  47019