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Theorem eqcomx 52
 Description: Commutativity of equality. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
eqcomx.1
eqcomx.2
eqcomx.3
Assertion
Ref Expression
eqcomx

Proof of Theorem eqcomx
StepHypRef Expression
1 eqcomx.3 . . . 4
21ax-cb1 29 . . 3
3 eqcomx.1 . . . 4
43ax-refl 42 . . 3
52, 4a1i 28 . 2
6 weq 41 . . . . . 6
76ax-refl 42 . . . . 5
82, 7a1i 28 . . . 4
9 eqcomx.2 . . . . 5
106, 6, 3, 9ax-ceq 51 . . . 4
118, 1, 10syl2anc 19 . . 3
126, 3wc 50 . . . 4
136, 9wc 50 . . . 4
1412, 13, 3, 3ax-ceq 51 . . 3
1511, 5, 14syl2anc 19 . 2
165, 15ax-eqmp 45 1
 Colors of variables: type var term Syntax hints:   ht 2  hb 3  kc 5   ke 7   wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-trud 26  ax-cb1 29  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51 This theorem is referenced by:  mpbirx  53  eqcomi  79
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