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