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Theorem nfeqd 2503

Description: Hypothesis builder for equality. (Contributed by Mario Carneiro, 7-Oct-2016.)

**Hypotheses**
Ref	Expression
nfeqd.1
nfeqd.2

**Assertion**
Ref	Expression
nfeqd

Proof of Theorem nfeqd Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfcleq 2347	. 2
2		nfv 1619	. . 3
3		nfeqd.1	. . . . 5
4	3	nfcrd 2502	. . . 4
5		nfeqd.2	. . . . 5
6	5	nfcrd 2502	. . . 4
7	4, 6	nfbid 1832	. . 3
8	2, 7	nfald 1852	. 2
9	1, 8	nfxfrd 1571	1

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176

wal 1540

wnf 1544

wceq 1642

wcel 1710

wnfc 2476

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 df-cleq 2346 df-nfc 2478

This theorem is referenced by: nfeld 2504 nfned 2612 vtoclgft 2905 sbcralt 3118 csbiebt 3172 dfnfc2 3909 nfiotad 4342 iota2df 4365 dfid3 4768 oprabid 5550