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Theorem nffvmpt1 5214
Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016.)
Assertion
Ref Expression
nffvmpt1  |-  F/_ x
( ( x  e.  A  |->  B ) `  C )
Distinct variable group:    x, C
Allowed substitution hints:    A( x)    B( x)

Proof of Theorem nffvmpt1
StepHypRef Expression
1 nfmpt1 3878 . 2  |-  F/_ x
( x  e.  A  |->  B )
2 nfcv 2194 . 2  |-  F/_ x C
31, 2nffv 5213 1  |-  F/_ x
( ( x  e.  A  |->  B ) `  C )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2181    |-> cmpt 3846   ` cfv 4930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-opab 3847  df-mpt 3848  df-iota 4895  df-fv 4938
This theorem is referenced by:  fvmptt  5290  fmptco  5358  offval2  5754  ofrfval2  5755  dom2lem  6283
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