Theorem opreqan12rd 4903

Description: Equality deduction for operation value.

Hypotheses

Ref	Expression
opreq1d.1	|- (ph -> A = B)
opreqan12i.2	|- (ps -> C = D)

Assertion

Ref	Expression
opreqan12rd	|- ((ps /\ ph) -> (AFC) = (BFD))

Proof of Theorem opreqan12rd

Step	Hyp	Ref	Expression
1		opreq1d.1	. . 3 |- (ph -> A = B)
2		opreqan12i.2	. . 3 |- (ps -> C = D)
3	1, 2	opreqan12d 4902	. 2 |- ((ph /\ ps) -> (AFC) = (BFD))
4	3	ancoms 484	1 |- ((ps /\ ph) -> (AFC) = (BFD))

Syntax hints:   -> wi 3   /\ wa 240   = wceq 1298  (class class class)co 4884

This theorem is referenced by:  mulgt0sr 6366  mulcnsr 6406  mulresr 6409  recdiv 6967  seq1res 7740  seqzfveq 7797  fsumcom 8288  nonbooli 11231  0cnop 11540  0cnfn 11541  idcnop 11542  idfisf 15189  reparpht 16065

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-14 1312  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865  ax-sep 3438  ax-nul 3445  ax-pow 3481  ax-pr 3524

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-eu 1775  df-mo 1776  df-clab 1872  df-cleq 1877  df-clel 1880  df-ne 2019  df-rex 2110  df-v 2294  df-dif 2597  df-un 2600  df-in 2603  df-ss 2605  df-nul 2876  df-pw 3035  df-sn 3049  df-pr 3050  df-op 3053  df-uni 3178  df-br 3339  df-opab 3396  df-xp 4000  df-cnv 4002  df-dm 4004  df-rn 4005  df-res 4006  df-ima 4007  df-fv 4014  df-opr 4886

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