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Theorem eqtypri 81
Description: Deduce equality of types from equality of expressions. (This is unnecessary but eliminates a lot of hypotheses.) (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
eqtypri.1 |- A:al
eqtypri.2 |- R |= [B = A]
Assertion
Ref Expression
eqtypri |- B:al

Proof of Theorem eqtypri
StepHypRef Expression
1 eqtypri.1 . 2 |- A:al
2 eqtypri.2 . 2 |- R |= [B = A]
31, 2ax-eqtypri 80 1 |- B:al
Colors of variables: type var term
Syntax hints:   = ke 7  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12
This theorem was proved from axioms:  ax-eqtypri 80
This theorem is referenced by:  mpbir  87  3eqtr4i  96  hbc  110  wal  134  wfal  135  wan  136  wim  137  wnot  138  wex  139  wor  140  weu  141
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