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Theorem pncan3oi 7795
 Description: Subtraction and addition of equals. Almost but not exactly the same as pncan3i 7856 and pncan 7785, this order happens often when applying "operations to both sides" so create a theorem specifically for it. A deduction version of this is available as pncand 7891. (Contributed by David A. Wheeler, 11-Oct-2018.)
Hypotheses
Ref Expression
pncan3oi.1
pncan3oi.2
Assertion
Ref Expression
pncan3oi

Proof of Theorem pncan3oi
StepHypRef Expression
1 pncan3oi.1 . 2
2 pncan3oi.2 . 2
3 pncan 7785 . 2
41, 2, 3mp2an 418 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   wcel 1445  (class class class)co 5690  cc 7445   caddc 7450   cmin 7750 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-14 1457  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978  ax-pow 4030  ax-pr 4060  ax-setind 4381  ax-resscn 7534  ax-1cn 7535  ax-icn 7537  ax-addcl 7538  ax-addrcl 7539  ax-mulcl 7540  ax-addcom 7542  ax-addass 7544  ax-distr 7546  ax-i2m1 7547  ax-0id 7550  ax-rnegex 7551  ax-cnre 7553 This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-fal 1302  df-nf 1402  df-sb 1700  df-eu 1958  df-mo 1959  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ne 2263  df-ral 2375  df-rex 2376  df-reu 2377  df-rab 2379  df-v 2635  df-sbc 2855  df-dif 3015  df-un 3017  df-in 3019  df-ss 3026  df-pw 3451  df-sn 3472  df-pr 3473  df-op 3475  df-uni 3676  df-br 3868  df-opab 3922  df-id 4144  df-xp 4473  df-rel 4474  df-cnv 4475  df-co 4476  df-dm 4477  df-iota 5014  df-fun 5051  df-fv 5057  df-riota 5646  df-ov 5693  df-oprab 5694  df-mpt2 5695  df-sub 7752 This theorem is referenced by:  mvrraddi  7796  mvlladdi  7797  resqrexlemcalc1  10562
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