Metamath Proof Explorer

Theorem mdandyvr14

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 mdandyvr14.1 ⊢φ↔ζ
mdandyvr14.2 ⊢ψ↔σ
mdandyvr14.3 ⊢χ↔φ
mdandyvr14.4 ⊢θ↔ψ
mdandyvr14.5 ⊢τ↔ψ
mdandyvr14.6 ⊢η↔ψ
Assertion mdandyvr14 ⊢χ↔ζ∧θ↔σ∧τ↔σ∧η↔σ

Proof

Step Hyp Ref Expression
1 mdandyvr14.1 ⊢φ↔ζ
2 mdandyvr14.2 ⊢ψ↔σ
3 mdandyvr14.3 ⊢χ↔φ
4 mdandyvr14.4 ⊢θ↔ψ
5 mdandyvr14.5 ⊢τ↔ψ
6 mdandyvr14.6 ⊢η↔ψ
7 2 1 3 4 5 6 mdandyvr1 ⊢χ↔ζ∧θ↔σ∧τ↔σ∧η↔σ