Theorem nfeq1 2402

Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfeq1	⊢ Ⅎ𝑥 𝐴 = 𝐵

Distinct variable group:   𝑥,𝐵

Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfeq1

Step	Hyp	Ref	Expression
1		nfeq1.1	. 2 ⊢ Ⅎ𝑥𝐴
2		nfcv 2392	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2400	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

This proof depends on syntax axioms:   = wceq 1402  Ⅎwnf 1513  Ⅎwnfc 2379

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-cleq 2231  df-clel 2234  df-nfc 2381

This theorem is used by:  euabsn  3781  invdisjrab  4124  fvmptt  5797  eusvobj2  6071  ovmpodv2  6222  ovi3  6226  dom2lem  7058  seq3f1olemstep  10951  seq3f1olemp  10952  fsumf1o  12157  isumss  12158  isummulc2  12193  fsum00  12229  isumshft  12257  fprodf1o  12355  prodssdc  12356