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Theorem mpteq2dva 3838
 Description: Slightly more general equality inference for the maps to notation. (Contributed by Scott Fenton, 25-Apr-2012.)
Hypothesis
Ref Expression
mpteq2dva.1 ((φ x A) → B = 𝐶)
Assertion
Ref Expression
mpteq2dva (φ → (x AB) = (x A𝐶))
Distinct variable group:   φ,x
Allowed substitution hints:   A(x)   B(x)   𝐶(x)

Proof of Theorem mpteq2dva
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 mpteq2dva.1 . 2 ((φ x A) → B = 𝐶)
31, 2mpteq2da 3837 1 (φ → (x AB) = (x A𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   = wceq 1242   ∈ wcel 1390   ↦ cmpt 3809 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-opab 3810  df-mpt 3811 This theorem is referenced by:  mpteq2dv  3839  fmptapd  5297  offval  5661  offval2  5668  caofinvl  5675  caofcom  5676  freceq1  5919  freceq2  5920
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