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Theorem spimd 13002
Description: Deduction form of spim 1716. (Contributed by BJ, 17-Oct-2019.)
Hypotheses
Ref Expression
spimd.nf  |-  ( ph  ->  F/ x ch )
spimd.1  |-  ( ph  ->  A. x ( x  =  y  ->  ( ps  ->  ch ) ) )
Assertion
Ref Expression
spimd  |-  ( ph  ->  ( A. x ps 
->  ch ) )

Proof of Theorem spimd
StepHypRef Expression
1 spimd.nf . 2  |-  ( ph  ->  F/ x ch )
2 spimd.1 . 2  |-  ( ph  ->  A. x ( x  =  y  ->  ( ps  ->  ch ) ) )
3 spimt 1714 . 2  |-  ( ( F/ x ch  /\  A. x ( x  =  y  ->  ( ps  ->  ch ) ) )  ->  ( A. x ps  ->  ch ) )
41, 2, 3syl2anc 408 1  |-  ( ph  ->  ( A. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329   F/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-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  2spim  13003
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