Theorem bdceqir 15490

Description: A class equal to a bounded one is bounded. Stated with a commuted (compared with bdceqi 15489) equality in the hypothesis, to work better with definitions ( B is the definiendum that one wants to prove bounded; see comment of bd0r 15471). (Contributed by BJ, 3-Oct-2019.)

Hypotheses

Ref	Expression
bdceqir.min	|- BOUNDED A
bdceqir.maj	|- B = A

Assertion

Ref	Expression
bdceqir	|- BOUNDED B

Proof of Theorem bdceqir

Step	Hyp	Ref	Expression
1		bdceqir.min	. 2 |- BOUNDED A
2		bdceqir.maj	. . 3 |- B = A
3	2	eqcomi 2200	. 2 |- A = B
4	1, 3	bdceqi 15489	1 |- BOUNDED B

Syntax hints:   = wceq 1364  BOUNDED wbdc 15486

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-bd0 15459

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192  df-bdc 15487

This theorem is referenced by:  bdcrab  15498  bdccsb  15506  bdcdif  15507  bdcun  15508  bdcin  15509  bdcnulALT  15512  bdcpw  15515  bdcsn  15516  bdcpr  15517  bdctp  15518  bdcuni  15522  bdcint  15523  bdciun  15524  bdciin  15525  bdcsuc  15526  bdcriota  15529