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Theorem nffvmpt1 5533
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 4109 . 2  |-  F/_ x
( x  e.  A  |->  B )
2 nfcv 2419 . 2  |-  F/_ x C
31, 2nffv 5532 1  |-  F/_ x
( ( x  e.  A  |->  B ) `  C )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406    e. cmpt 4077   ` cfv 5255
This theorem is referenced by:  invfuc  13848  yonedalem4b  14050  limcmpt  19233  lhop2  19362  fmuldfeq  27713
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-iota 5219  df-fv 5263
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