Theorem oprabbid 6350

Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 24-Jun-2014.)

Hypotheses

Ref	Expression
oprabbid.1
oprabbid.2
oprabbid.3
oprabbid.4

Assertion

Ref	Expression
oprabbid

Distinct variable groups:   ,   ,

Proof of Theorem oprabbid

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		oprabbid.1	. . . 4
2		oprabbid.2	. . . . 5
3		oprabbid.3	. . . . . 6
4		oprabbid.4	. . . . . . 7
5	4	anbi2d 703	. . . . . 6
6	3, 5	exbid 1886	. . . . 5
7	2, 6	exbid 1886	. . . 4
8	1, 7	exbid 1886	. . 3
9	8	abbidv 2593	. 2
10		df-oprab 6300	. 2
11		df-oprab 6300	. 2
12	9, 10, 11	3eqtr4g 2523	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  {cab 2442  <.cop 4035  {coprab 6297

This theorem is referenced by:  oprabbidv  6351  mpt2eq123  6356

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-oprab 6300