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Theorem 2spim 13057
 Description: Double substitution, as in spim 1716. (Contributed by BJ, 17-Oct-2019.)
Hypotheses
Ref Expression
2spim.nfx
2spim.nfz
2spim.1
Assertion
Ref Expression
2spim
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem 2spim
StepHypRef Expression
1 2spim.nfz . 2
2 2spim.nfx . . . 4
32a1i 9 . . 3
4 2spim.1 . . . . 5
54expcom 115 . . . 4
65alrimiv 1846 . . 3
73, 6spimd 13056 . 2
81, 7spim 1716 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1329  wnf 1436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  ch2var  13058
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