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Axiom ax-1c 4081
Description: State the axiom of cardinal one. This axiom guarantees the existence of the set of all singletons, which will become cardinal one later in our development. Axiom P8 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ax-1c xy(y xzw(w yw = z))
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Axiom ax-1c
StepHypRef Expression
1 vy . . . . 5 set y
2 vx . . . . 5 set x
31, 2wel 1711 . . . 4 wff y x
4 vw . . . . . . . 8 set w
54, 1wel 1711 . . . . . . 7 wff w y
6 vz . . . . . . . 8 set z
74, 6weq 1643 . . . . . . 7 wff w = z
85, 7wb 176 . . . . . 6 wff (w yw = z)
98, 4wal 1540 . . . . 5 wff w(w yw = z)
109, 6wex 1541 . . . 4 wff zw(w yw = z)
113, 10wb 176 . . 3 wff (y xzw(w yw = z))
1211, 1wal 1540 . 2 wff y(y xzw(w yw = z))
1312, 2wex 1541 1 wff xy(y xzw(w yw = z))
Colors of variables: wff set class
This axiom is referenced by:  1cex  4142
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