Metamath Proof Explorer


Theorem oveqdr

Description: Equality of two operations for any two operands. Useful in proofs using *propd theorems. (Contributed by Mario Carneiro, 29-Jun-2015)

Ref Expression
Hypothesis oveqdr.1 φ F = G
Assertion oveqdr φ ψ x F y = x G y

Proof

Step Hyp Ref Expression
1 oveqdr.1 φ F = G
2 1 oveqd φ x F y = x G y
3 2 adantr φ ψ x F y = x G y