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

Step	Hyp	Ref	Expression
1		eqtypri.1	. 2 |- A:al
2		eqtypri.2	. 2 |- R |= [B = A]
3	1, 2	ax-eqtypri 80	1 |- B:al

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