Metamath Proof Explorer


Theorem mdandyv3

Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ph, ps accordingly. (Contributed by Jarvin Udandy, 6-Sep-2016)

Ref Expression
Hypotheses mdandyv3.1 φ
mdandyv3.2 ψ
mdandyv3.3 χ
mdandyv3.4 θ
mdandyv3.5 τ
mdandyv3.6 η
Assertion mdandyv3 χψθψτφηφ

Proof

Step Hyp Ref Expression
1 mdandyv3.1 φ
2 mdandyv3.2 ψ
3 mdandyv3.3 χ
4 mdandyv3.4 θ
5 mdandyv3.5 τ
6 mdandyv3.6 η
7 3 2 bothtbothsame χψ
8 4 2 bothtbothsame θψ
9 7 8 pm3.2i χψθψ
10 5 1 bothfbothsame τφ
11 9 10 pm3.2i χψθψτφ
12 6 1 bothfbothsame ηφ
13 11 12 pm3.2i χψθψτφηφ