Theorem ineccnvmo2 34125

Description: Lemma for ~? dffunsALTV5 and ~? dffunALTV5 (via ~? cossssid5 ). (Contributed by Peter Mazsa, 4-Sep-2021.)

Assertion

Ref	Expression
ineccnvmo2	|- ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) <-> A. u E* x u F x )

Distinct variable group:   u, F, x, y

Proof of Theorem ineccnvmo2

Step	Hyp	Ref	Expression
1		ineccnvmo 34122	. 2 |- ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) <-> A. u E* x e. ran F u F x )
2		alrmomo 34123	. 2 |- ( A. u E* x e. ran F u F x <-> A. u E* x u F x )
3	1, 2	bitri 264	1 |- ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) <-> A. u E* x u F x )

Syntax hints:   <-> wb 196   \/ wo 383   A.wal 1481   = wceq 1483   E*wmo 2471   A.wral 2912   E*wrmo 2915   i^i cin 3573   (/)c0 3915   class class class wbr 4653   `'ccnv 5113   ran crn 5115   [cec 7740

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-rmo 2920  df-rab 2921  df-v 3202  df-sbc 3436  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654  df-opab 4713  df-xp 5120  df-rel 5121  df-cnv 5122  df-dm 5124  df-rn 5125  df-res 5126  df-ima 5127  df-ec 7744

This theorem is referenced by: (None)