Metamath Proof Explorer


Theorem parteq1d

Description: Equality theorem for partition, deduction version. (Contributed by Peter Mazsa, 5-Oct-2021)

Ref Expression
Hypothesis parteq1d.1 φR=S
Assertion parteq1d Could not format assertion : No typesetting found for |- ( ph -> ( R Part A <-> S Part A ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 parteq1d.1 φR=S
2 parteq1 Could not format ( R = S -> ( R Part A <-> S Part A ) ) : No typesetting found for |- ( R = S -> ( R Part A <-> S Part A ) ) with typecode |-
3 1 2 syl Could not format ( ph -> ( R Part A <-> S Part A ) ) : No typesetting found for |- ( ph -> ( R Part A <-> S Part A ) ) with typecode |-