Metamath Proof Explorer

Theorem mdandyvr11

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 mdandyvr11.1 ⊢φ↔ζ
mdandyvr11.2 ⊢ψ↔σ
mdandyvr11.3 ⊢χ↔ψ
mdandyvr11.4 ⊢θ↔ψ
mdandyvr11.5 ⊢τ↔φ
mdandyvr11.6 ⊢η↔ψ
Assertion mdandyvr11 ⊢χ↔σ∧θ↔σ∧τ↔ζ∧η↔σ

Proof

Step Hyp Ref Expression
1 mdandyvr11.1 ⊢φ↔ζ
2 mdandyvr11.2 ⊢ψ↔σ
3 mdandyvr11.3 ⊢χ↔ψ
4 mdandyvr11.4 ⊢θ↔ψ
5 mdandyvr11.5 ⊢τ↔φ
6 mdandyvr11.6 ⊢η↔ψ
7 2 1 3 4 5 6 mdandyvr4 ⊢χ↔σ∧θ↔σ∧τ↔ζ∧η↔σ