Theorem mdandyvrx15 44502

Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)

Hypotheses

Ref	Expression
mdandyvrx15.1	⊢ (𝜑 ⊻ 𝜁)
mdandyvrx15.2	⊢ (𝜓 ⊻ 𝜎)
mdandyvrx15.3	⊢ (𝜒 ↔ 𝜓)
mdandyvrx15.4	⊢ (𝜃 ↔ 𝜓)
mdandyvrx15.5	⊢ (𝜏 ↔ 𝜓)
mdandyvrx15.6	⊢ (𝜂 ↔ 𝜓)

Assertion

Ref	Expression
mdandyvrx15	⊢ ((((𝜒 ⊻ 𝜎) ∧ (𝜃 ⊻ 𝜎)) ∧ (𝜏 ⊻ 𝜎)) ∧ (𝜂 ⊻ 𝜎))

Proof of Theorem mdandyvrx15

Step	Hyp	Ref	Expression
1		mdandyvrx15.2	. 2 ⊢ (𝜓 ⊻ 𝜎)
2		mdandyvrx15.1	. 2 ⊢ (𝜑 ⊻ 𝜁)
3		mdandyvrx15.3	. 2 ⊢ (𝜒 ↔ 𝜓)
4		mdandyvrx15.4	. 2 ⊢ (𝜃 ↔ 𝜓)
5		mdandyvrx15.5	. 2 ⊢ (𝜏 ↔ 𝜓)
6		mdandyvrx15.6	. 2 ⊢ (𝜂 ↔ 𝜓)
7	1, 2, 3, 4, 5, 6	mdandyvrx0 44487	1 ⊢ ((((𝜒 ⊻ 𝜎) ∧ (𝜃 ⊻ 𝜎)) ∧ (𝜏 ⊻ 𝜎)) ∧ (𝜂 ⊻ 𝜎))

Syntax hints:   ↔ wb 205   ∧ wa 396   ⊻ wxo 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-xor 1507

This theorem is referenced by: (None)