Metamath Proof Explorer


Theorem funeqd

Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013)

Ref Expression
Hypothesis funeqd.1 φ A = B
Assertion funeqd φ Fun A Fun B

Proof

Step Hyp Ref Expression
1 funeqd.1 φ A = B
2 funeq A = B Fun A Fun B
3 1 2 syl φ Fun A Fun B