mpteq2ia - New Foundations Explorer

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Theorem mpteq2ia 5659

Description: An equality inference for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)

**Hypothesis**
Ref	Expression
mpteq2ia.1

**Assertion**
Ref	Expression
mpteq2ia

**Proof of Theorem mpteq2ia**
Step	Hyp	Ref	Expression
1		eqid 2353	. . 3
2	1	ax-gen 1546	. 2
3		mpteq2ia.1	. . 3
4	3	rgen 2679	. 2
5		mpteq12f 5655	. 2 $/\$
6	2, 4, 5	mp2an 653	1

Colors of variables: wff setvar class

Syntax hints:

wi 4

wal 1540

wceq 1642

wcel 1710

wral 2614

cmpt 5651

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-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-ral 2619 df-opab 4623 df-mpt 5652

This theorem is referenced by: mpteq2i 5660