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Theorem oprabbii 5565

Description: Equivalent wff's yield equal operation class abstractions. (Unnecessary distinct variable restrictions were removed by David Abernethy, 19-Jun-2012.) (Contributed by set.mm contributors, 28-May-1995.) (Revised by set.mm contributors, 24-Jul-2012.)

Hypothesis

Ref	Expression
oprabbii.1

Assertion

Ref	Expression
oprabbii

Distinct variable groups:   ,   , Allowed substitution hints:   (,,)   (,,)

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Proof of Theorem oprabbii Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eqid 2353	. 2
2		oprabbii.1	. . . 4
3	2	a1i 10	. . 3
4	3	oprabbidv 5564	. 2
5	1, 4	ax-mp 8	1

Colors of variables: wff setvar class

Syntax hints:   wb 176   wceq 1642  coprab 5527

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-oprab 5528

This theorem is referenced by:  oprab4  5566  oprabbi2i  5647  mpt2v  5719

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