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:α
eqtypri.2	⊢ R⊧[B = A]

Assertion

Ref	Expression
eqtypri	⊢ B:α

Proof of Theorem eqtypri

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

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