Metamath Proof Explorer

Theorem mdandyvr12

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 mdandyvr12.1 ⊢φ↔ζ
mdandyvr12.2 ⊢ψ↔σ
mdandyvr12.3 ⊢χ↔φ
mdandyvr12.4 ⊢θ↔φ
mdandyvr12.5 ⊢τ↔ψ
mdandyvr12.6 ⊢η↔ψ
Assertion mdandyvr12 ⊢χ↔ζ∧θ↔ζ∧τ↔σ∧η↔σ

Proof

Step Hyp Ref Expression
1 mdandyvr12.1 ⊢φ↔ζ
2 mdandyvr12.2 ⊢ψ↔σ
3 mdandyvr12.3 ⊢χ↔φ
4 mdandyvr12.4 ⊢θ↔φ
5 mdandyvr12.5 ⊢τ↔ψ
6 mdandyvr12.6 ⊢η↔ψ
7 2 1 3 4 5 6 mdandyvr3 ⊢χ↔ζ∧θ↔ζ∧τ↔σ∧η↔σ