Theorem bothtbothsame 48063

Description: Given both a, b are equivalent to ⊤, there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016.)

Hypotheses

Ref	Expression
bothtbothsame.1	⊢ (𝜑 ↔ ⊤)
bothtbothsame.2	⊢ (𝜓 ↔ ⊤)

Assertion

Ref	Expression
bothtbothsame	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem bothtbothsame

Step	Hyp	Ref	Expression
1		bothtbothsame.1	. 2 ⊢ (𝜑 ↔ ⊤)
2		bothtbothsame.2	. 2 ⊢ (𝜓 ↔ ⊤)
3	1, 2	bitr4i 281	1 ⊢ (𝜑 ↔ 𝜓)

This proof depends on syntax axioms:   ↔ wb 209  ⊤wtru 1570

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  mdandyv1  48114  mdandyv2  48115  mdandyv3  48116  mdandyv4  48117  mdandyv5  48118  mdandyv6  48119  mdandyv7  48120  mdandyv8  48121  mdandyv9  48122  mdandyv10  48123  mdandyv11  48124  mdandyv12  48125  mdandyv13  48126  mdandyv14  48127  mdandyv15  48128  dandysum2p2e4  48162