eqeqan12d - New Foundations Explorer

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Theorem eqeqan12d 2368

Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 9-Aug-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.)

**Hypotheses**
Ref	Expression
eqeqan12d.1
eqeqan12d.2

**Assertion**
Ref	Expression
eqeqan12d	$/\$

**Proof of Theorem eqeqan12d**
Step	Hyp	Ref	Expression
1		eqeqan12d.1	. 2
2		eqeqan12d.2	. 2
3		eqeq12 2365	. 2 $/\$
4	1, 2, 3	syl2an 463	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176 $/\$ wa 358

wceq 1642

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

This theorem is referenced by: eqeqan12rd 2369 adj11 3889 pw1equn 4331 pw1eqadj 4332 eqfnfv2 5393 pw1fnf1o 5855 dflec2 6210 tc11 6228

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