eleq1a - New Foundations Explorer

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Theorem eleq1a 2422

Description: A transitive-type law relating membership and equality. (Contributed by NM, 9-Apr-1994.)

**Assertion**
Ref	Expression
eleq1a

**Proof of Theorem eleq1a**
Step	Hyp	Ref	Expression
1		eleq1 2413	. 2
2	1	biimprcd 216	1

Colors of variables: wff setvar class

Syntax hints:

wi 4

wceq 1642

wcel 1710

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-11 1746 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-cleq 2346 df-clel 2349

This theorem is referenced by: elex22 2870 elex2 2871 reu6 3025 disjne 3596 evennn 4506 oddnn 4507 nnadjoin 4520 phi11lem1 4595 f1o2d 5727