Metamath Proof Explorer

Theorem mdandyvr9

Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016)

Ref Expression
Hypotheses mdandyvr9.1 ⊢φ↔ζ
mdandyvr9.2 ⊢ψ↔σ
mdandyvr9.3 ⊢χ↔ψ
mdandyvr9.4 ⊢θ↔φ
mdandyvr9.5 ⊢τ↔φ
mdandyvr9.6 ⊢η↔ψ
Assertion mdandyvr9 ⊢χ↔σ∧θ↔ζ∧τ↔ζ∧η↔σ

Proof

Step Hyp Ref Expression
1 mdandyvr9.1 ⊢φ↔ζ
2 mdandyvr9.2 ⊢ψ↔σ
3 mdandyvr9.3 ⊢χ↔ψ
4 mdandyvr9.4 ⊢θ↔φ
5 mdandyvr9.5 ⊢τ↔φ
6 mdandyvr9.6 ⊢η↔ψ
7 2 1 3 4 5 6 mdandyvr6 ⊢χ↔σ∧θ↔ζ∧τ↔ζ∧η↔σ