Theorem infeq1i 7272

Description: Equality inference for infimum. (Contributed by AV, 2-Sep-2020.)

Hypothesis

Ref	Expression
infeq1i.1	|- B = C

Assertion

Ref	Expression
infeq1i	|- inf ( B , A , R ) = inf ( C , A , R )

Proof of Theorem infeq1i

Step	Hyp	Ref	Expression
1		infeq1i.1	. 2 |- B = C
2		infeq1 7270	. 2 |- ( B = C -> inf ( B , A , R ) = inf ( C , A , R ) )
3	1, 2	ax-mp 5	1 |- inf ( B , A , R ) = inf ( C , A , R )

Syntax hints:   = wceq 1398  infcinf 7242

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-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-ral 2516  df-rex 2517  df-rab 2520  df-uni 3899  df-sup 7243  df-inf 7244

This theorem is referenced by:  mincom  11869  xrbdtri  11916  nninfctlemfo  12691  lcmcom  12716  lcmass  12737