Theorem eqmiddle-P6.CL 709

Description: Closed Form of eqmiddle-P6 708.

'𝑦' cannot occur in '𝑡'.

Assertion

Ref	Expression
eqmiddle-P6.CL	⊢ (𝑥 = 𝑡 → ∃𝑦(𝑥 = 𝑦 ∧ 𝑦 = 𝑡))

Distinct variable groups:   𝑡,𝑦   𝑥,𝑦

Proof of Theorem eqmiddle-P6.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (𝑥 = 𝑡 → 𝑥 = 𝑡)
2	1	eqmiddle-P6 708	1 ⊢ (𝑥 = 𝑡 → ∃𝑦(𝑥 = 𝑦 ∧ 𝑦 = 𝑡))

Syntax hints:  term-obj 1   = wff-equals 6   → wff-imp 10   ∧ wff-and 132  ∃wff-exists 595

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18  ax-L7 19

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596

This theorem is referenced by:  trnsvsubw-P6  710  trnsvsub-P6  763