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Theorem 2spim 9241
Description: Double substitution, as in spim 1623. (Contributed by BJ, 17-Oct-2019.)
Hypotheses
Ref Expression
2spim.nfx  F/
2spim.nfz  F/
2spim.1  t
Assertion
Ref Expression
2spim
Distinct variable groups:   ,   , t
Allowed substitution hints:   (,,, t)   (,,, t)

Proof of Theorem 2spim
StepHypRef Expression
1 2spim.nfz . 2  F/
2 2spim.nfx . . . 4  F/
32a1i 9 . . 3  t  F/
4 2spim.1 . . . . 5  t
54expcom 109 . . . 4  t
65alrimiv 1751 . . 3  t
73, 6spimd 9240 . 2  t
81, 7spim 1623 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   F/wnf 1346
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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  ch2var  9242
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