Theorem syldan 36

Description: Syllogism inference. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypotheses

Ref	Expression
syldan.1	|- (R, S) |= T
syldan.2	|- (R, T) |= A

Assertion

Ref	Expression
syldan	|- (R, S) |= A

Proof of Theorem syldan

Step	Hyp	Ref	Expression
1		syldan.1	. . . . 5 |- (R, S) |= T
2	1	ax-cb1 29	. . . 4 |- (R, S):*
3	2	wctl 33	. . 3 |- R:*
4	2	wctr 34	. . 3 |- S:*
5	3, 4	simpl 22	. 2 |- (R, S) |= R
6		syldan.2	. 2 |- (R, T) |= A
7	5, 1, 6	syl2anc 19	1 |- (R, S) |= A

Syntax hints:  kct 10   |= wffMMJ2 11

This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-cb1 29  ax-wctl 31  ax-wctr 32

This theorem is referenced by:  alimdv  184