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Definition df-swap 4724
 Description: Define a function that swaps the two elements of an ordered pair. (Contributed by SF, 5-Jan-2015.)
Assertion
Ref Expression
df-swap Swap = {x, y zw(x = z, w y = w, z)}
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Definition df-swap
StepHypRef Expression
1 cswap 4718 . 2 class Swap
2 vx . . . . . . . 8 setvar x
32cv 1641 . . . . . . 7 class x
4 vz . . . . . . . . 9 setvar z
54cv 1641 . . . . . . . 8 class z
6 vw . . . . . . . . 9 setvar w
76cv 1641 . . . . . . . 8 class w
85, 7cop 4561 . . . . . . 7 class z, w
93, 8wceq 1642 . . . . . 6 wff x = z, w
10 vy . . . . . . . 8 setvar y
1110cv 1641 . . . . . . 7 class y
127, 5cop 4561 . . . . . . 7 class w, z
1311, 12wceq 1642 . . . . . 6 wff y = w, z
149, 13wa 358 . . . . 5 wff (x = z, w y = w, z)
1514, 6wex 1541 . . . 4 wff w(x = z, w y = w, z)
1615, 4wex 1541 . . 3 wff zw(x = z, w y = w, z)
1716, 2, 10copab 4622 . 2 class {x, y zw(x = z, w y = w, z)}
181, 17wceq 1642 1 wff Swap = {x, y zw(x = z, w y = w, z)}
 Colors of variables: wff setvar class This definition is referenced by:  elswap  4740  brswap2  4860  brswap  5509  dfswap3  5728
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