Metamath Proof Explorer

Theorem mdandyvr13

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 mdandyvr13.1 ⊢ φ ↔ ζ
mdandyvr13.2 ⊢ ψ ↔ σ
mdandyvr13.3 ⊢ χ ↔ ψ
mdandyvr13.4 ⊢ θ ↔ φ
mdandyvr13.5 ⊢ τ ↔ ψ
mdandyvr13.6 ⊢ η ↔ ψ
Assertion mdandyvr13 ⊢ χ ↔ σ ∧ θ ↔ ζ ∧ τ ↔ σ ∧ η ↔ σ

Proof

Step Hyp Ref Expression
1 mdandyvr13.1 ⊢ φ ↔ ζ
2 mdandyvr13.2 ⊢ ψ ↔ σ
3 mdandyvr13.3 ⊢ χ ↔ ψ
4 mdandyvr13.4 ⊢ θ ↔ φ
5 mdandyvr13.5 ⊢ τ ↔ ψ
6 mdandyvr13.6 ⊢ η ↔ ψ
7 2 1 3 4 5 6 mdandyvr2 ⊢ χ ↔ σ ∧ θ ↔ ζ ∧ τ ↔ σ ∧ η ↔ σ