Metamath Proof Explorer

Theorem mdandyvr10

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 mdandyvr10.1 ⊢ φ ↔ ζ
mdandyvr10.2 ⊢ ψ ↔ σ
mdandyvr10.3 ⊢ χ ↔ φ
mdandyvr10.4 ⊢ θ ↔ ψ
mdandyvr10.5 ⊢ τ ↔ φ
mdandyvr10.6 ⊢ η ↔ ψ
Assertion mdandyvr10 ⊢ χ ↔ ζ ∧ θ ↔ σ ∧ τ ↔ ζ ∧ η ↔ σ

Proof

Step Hyp Ref Expression
1 mdandyvr10.1 ⊢ φ ↔ ζ
2 mdandyvr10.2 ⊢ ψ ↔ σ
3 mdandyvr10.3 ⊢ χ ↔ φ
4 mdandyvr10.4 ⊢ θ ↔ ψ
5 mdandyvr10.5 ⊢ τ ↔ φ
6 mdandyvr10.6 ⊢ η ↔ ψ
7 2 1 3 4 5 6 mdandyvr5 ⊢ χ ↔ ζ ∧ θ ↔ σ ∧ τ ↔ ζ ∧ η ↔ σ